propositional logic and set theory questions and answers pdf

They are not guaran-teed to be comprehensive of the material covered in the course. Propositional Logic Exercise 2.6. 17.7 Modal logic. The argument is valid if the premises imply the conclusion.An argument form is an argument that is valid no matter what propositions are substituted into its propositional variables. Let p stand for the proposition“I bought a lottery ticket”and q for“I won the jackpot”. Chapter 1.1-1.3 2 / 21 We need to convert the following sentence into a mathematical statement using propositional logic only. There are 40 questions. I Propositional logic I Propositional calculus I Predicate logic I Predicate calculus Section 2. /Filter /FlateDecode A contradiction is a compound statement that is always false A contingent statement is one that is neither a tautology nor a contradiction For example, the truth table of p v ~p shows it is a tautology. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. The use of the propositional logic has dramatically increased since the development of powerful search algo-rithms and implementation methods since the later 1990ies. Predicate logic can express these statements and make inferences on them. logic is relatively recent: the 19th century pioneers were Bolzano, Boole, Cantor, Dedekind, Frege, Peano, C.S. ... Let S be a set of students, R a set of college rooms, P a set of professors, and C a set of courses. 3.2.2: Link between logic and set theory Last updated; Save as PDF Page ID 10722; No headers. X > 3. ! Inductive logic is a very difficult and intricate subject, partly because the Solution for Q. 10 CHAPTER 1. C�w��p�n�z\��~�� iĭ;��gV�e��O��Bى϶��B{Η̏Jh��gK�d��;�k��ۅ�,��š_�R��u9��[�U�nğ8�u ��~�w�. Names and predicates 119 12. (Georg Cantor) In the previous chapters, we have often encountered "sets", for example, prime numbers form a set, domains in predicate logic form sets as well. ��p��r� 9\��ԡ�3+��w��Qs�Y�d`$�g@�. Also explore over 41 similar quizzes in this category. Complex issues arise in Set Theory more than any other area of pure mathematics; in particular, Mathematical Logic is used in … As opposed to predicate calculus, which will be studied in Chapter 4, the statements will not have quanti er symbols like 8, 9. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. Because of the close relationship between logic and set theory… ... Set Theory • A set … 17.3 Mathematical induction. The classical propositional logic is the most basic and most widely used logic. Let L ⊆ S × R be the relation containing (s,r) if student s lives in ... Set Theory • A set … How to prove it. Use the DPLL procedure to verify weather the following formula is satisﬁable: (p∨(¬q∧r))⊃((q∨¬r)⊃p) Exercise 3 (First order logic: representation). 1 Propositional calculus II Logic and Set Theory 1 Propositional calculus Propositional calculus is the study of logical statements such p)pand p) (q)p). Sorry, preview is currently unavailable. It is a tautology if it is always ... circuit to compute each bit of the answer separately. The Laws of Truth - Smith, Nicholas J. J. Departamento de Ingenierıa Eléctrica Sección de Computación, Propositional Logics of Dependence and Independence, Part I. Outline 1 Propositions 2 Logical Equivalences 3 Normal Forms Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Predicate Logic ! Summary of first order logic 173 Part III: A Look Forward 17. 1 Propositional calculus II Logic and Set Theory 1 Propositional calculus Propositional calculus is the study of logical statements such p)pand p) (q)p). Academia.edu no longer supports Internet Explorer. No. It is a notation for Boolean functions, together with several powerful proof and reasoning methods. Enter the email address you signed up with and we'll email you a reset link. Select the letter of the most appropriate answer and SHADE in the corresponding region of the answer sheet. I Propositional logic I Propositional calculus I Predicate logic I Predicate calculus Section 2. - Use the truth tables method to determine whether the formula ’: p^:q!p^q is a logical consequence of the formula : :p. All men are mortal. It is a notation for Boolean functions, together with several powerful proof and reasoning methods. www.gtu-mcq.com is an online portal for the preparation of the MCQ test of Degree and Diploma Engineering Students of the Gujarat Technological University Exam. If the correct answer is NOT one of the choices, mark "E" on teh answer sheet. The above statement cannot be adequately expressed using only propositional logic. PROPOSITIONAL LOGIC Starting at the end, when the waiter puts the third plate without asking, you see a major logical act ‘in broad daylight’: the waiter draws a conclusion. � ��T_t8�� L�o�F�H;NnbΧ}�p|��F��X�7;4ÿ��˱wŪ�Cy8u��m}�w��>�%�S��GG�s��՞�T��(��= ;р�~: �8�~��њ�X��ʳnj>#��y_sC��LV�c��dr�ь��5��3��ϣ�U>�gu*��:��K��K�Z2e�~�7��`��O�b�b�g,��Ia�o��<4.�Pgm��\�R8`�e�O�M�1�WB*�~s��M_g��6l Summary of Propositional Logic 113 Part II: First Order Logic 11. Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry.He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. %PDF-1.4 For our purposes, it will sufﬁce to approach basic logical concepts informally. (Georg Cantor) In the previous chapters, we have often encountered "sets", for example, prime numbers form a set, domains in predicate logic form sets as well. It covers i) basic approaches to logic, including proof theory and especially model theory, ii) extensions of standard logic (such as modal logic) that are important in philosophy, and iii) some elementary philosophy of logic… 17.2 Axiomatic propositional logic. Propositional logic: • Propositional statement: expression that has a truth value (true/false). The information in the two answers received allows the waiter to infer automatically where the third dish must go. /�\��m:$ �R!�ڮ��z�� S�wB%��F�1��;Xϱ��0��ª��:d�X��/��;r�O.�[U;l��a��!v4C �d�+�zgh��+� They are not guaran-teed to be comprehensive of the material covered in the course. /Length 4423 stream SEEM 5750 7 Propositional logic A tautology is a compound statement that is always true. Let L ⊆ S × R be the relation containing (s,r) if student s lives in Exercise Sheet 1: Propositional Logic 1. SEEM 5750 7 Propositional logic A tautology is a compound statement that is always true. )��9��ڜ�{(��|G ��R��6 �$C�{R�9"=pD�sT��c��g�ΒnPo�'I��2C�#�frE0^M��\Z�)�Q��L��%�(�j�� These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. The use of the propositional logic has dramatically increased since the development of powerful search algo-rithms and implementation methods since the later 1990ies. X > 3. ! From our perspective we see their work as leading to boolean algebra, set theory, propositional logic, predicate logic, as clarifying the foundations of the natural and real number Some statements cannot be expressed in propositional logic, such as: ! ��z�%�-��Rt�￘J��0Ui��E��b� �t#3��R�)�ъ��o�#R�Z�s��v�#e�ThH[��S{�v��Ä��s�}C+2��j��x�s�f��Q�(�\�|"4��G6� The study of these topics is, in itself, a formidable task. Let p stand for the proposition“I bought a lottery ticket”and q for“I won the jackpot”. Exercise 2 (Propositional logic theory (Max 5 marks)). logic is relatively recent: the 19th century pioneers were Bolzano, Boole, Cantor, Dedekind, Frege, Peano, C.S. 2 ~x NOT y AND x x x y x /\ y x \/ y OR Figure 1: Types of gates in a digital circuit. PSU MATH RELAYS LOGIC & SET THEORY 2017 MULTIPLE CHOICE. ?� �9w��V�RΖ��k��*� v�5>�Yk��'�!��Nاo��Xv� {U2�q��c�]��)��O?Uhm�'Ռd��|}�4��Ӂj��j�e�Q$�6��F�`xq/��&��s ��{D�Mt�d��5t�F�{��z��%/��^�C)��[��Й��G��6}�@[�ml��_�G�c$w$�=C +��)O��M�*Z��`��%�r�-=z/>��w��Sp� N-σF+�p��"�(��,ʐNr��}� ��S�l��j�:%ӄho C��m�.��υ��8��&6! ... Let S be a set of students, R a set of college rooms, P a set of professors, and C a set of courses. 3 0 obj << “All” and “some” 127 13. You can download the paper by clicking the button above. ASWDC (App, Software & Website Development Center) Darshan Institute of Engineering & Technology (DIET) A labelled graph is a triple %V,A,L& where V is a set of vertex, A isa set of directed arcs between vertexes and L is a function that Predicate Logic ! Another way of stating this: induc-tive logic investigates arguments in which the truth of the premises makes likely the truth of the conclusion. One can study the standard semantics of classical propositional logic within classical logic set theory, so we can say that the semantics of classical logic is meta-theoretically "self-hosting". Introduction Consider the following example. Inductive logic investigates the process of drawing probable (likely, plausi-ble) though fallible conclusions from premises. How to prove it. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. Outline 1 Propositions 2 Logical Equivalences 3 Normal Forms Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Universal derivation 147 15. V��6z�x$��֦�W��G�W��&��ٺQ��Y��w.��÷��Z[�͈� 8��O@쑯� "Every person who is 18 years or older, is eligible to vote." PROPOSITIONAL LOGIC Starting at the end, when the waiter puts the third plate without asking, you see a major logical act ‘in broad daylight’: the waiter draws a conclusion. 2-2 CHAPTER 2. Ck jꬥ��0��kǀ)_d��HT�l"=fk��8��6�ѩd �T��Q�^�,�e��bO�F�C�d��,;LVI�X�A5b b3gX0�e��K��l,��!� ��rAY©��ӅF��{O�A� �)iK�w��B��6�'�B��3m� ! It is a tautology if it is always ... circuit to compute each bit of the answer separately. The continuum hypothesis is a statement in first-order (predicate) logic dealing with the standard Zermelo-Frankel (ZF) axioms of set theory. The argument is valid if the premises imply the conclusion.An argument form is an argument that is valid no matter what propositions are substituted into its propositional variables. 17.5 Set theory. We are going to use PL as our metalanguage to describe English (the object language)—in particular, the meaning of English sentences. Prerequisite : Introduction to Propositional Logic. Arguments in Propositional Logic A argument in propositional logic is a sequence of propositions.All but the final proposition are called premises.The last statement is the conclusion. x��[[o�ȕ~�_� Hps�^� ��$@�!�c�ݔęV��d[V6?>�R,^Tl�/��A$�ŪS�N��Kw��7��Ʃ��%d!�1ފ�.��_��cuw��ޭ�K��.�ru�>`��[��t��*��.��0�Oi\!��b�|ᕲ4�_��w�в:��-~�tp��\v06��˛fG�RA��J��4޷�O9�VAF w�@��AH��ɐ�VD These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. 3. Just as the laws of logic allow us to do algebra with logical formulas, the laws of set theory allow us to do algebra with sets. SET THEORY If we are interested in elements of a set A that are not contained in a set B, we can write this set as A ∩ B. 2 ~x NOT y AND x x x y x /\ y x \/ y OR Figure 1: Types of gates in a digital circuit. 10. Try this amazing Set Theory And Logic Quiz quiz which has been attempted 5218 times by avid quiz takers. A contradiction is a compound statement that is always false A contingent statement is one that is neither a tautology nor a contradiction For example, the truth table of p v ~p shows it is a tautology. 17.2 Axiomatic propositional logic. Some trees have needles. ~��>�K�qa��ٷ~8��grG\�#��1bFcS$ 3ʦi�6�� -��7��$g=�53�89�~hK�� 쐺�mb��rB�8T,��x�q�Znm��E�x��$��fQ��x-�[�ܑ�9�N��Dm�;�#�m��,Sl��`B�\?�C�s�&M��1�$�TҌ@ �`��׆�tH2��~s ��5�D�X|��'6��8pd �VY�-`2��2��#�c��^��0&��ƞő[&i��X9��d��m��t�o�ع3��hTl�㫘烗��0�W�k�N}��Ǚhv��#ML�a�&G��.�ڬR�h��.K��S�"��lRD�ゕ�&��~��!u��\��A�e��`\}��3�$�C�caH�S��YC��֍�.2rz��o��0U"�c>�.�t#�pe��@��ÒW��G>�m�8^_��8'�̈d)GLI��ķU�v;�v~��8SXA��B��v�ߥ�36��B��,��&f�G All men are mortal. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, … Another important operation is the union that represents the set of … collection of declarative statements that has either a truth value \"true” or a truth value \"false >> while p ^ ~p is a contradiction If a conditional is also a tautology, then it is called an implication This property is probably a big part of why classical logic is so easy to accept as the default/implicit background/foundational logic for mathematics. If Aand Brepresent two properties then A\Bis the set of those objects that have both properties. 17.4 The deduction theorem for propositional logic. 2-2 CHAPTER 2. Chapter 1.1-1.3 2 / 21 Propositional Logic (PL) 3.1. while p ^ ~p is a contradiction If a conditional is also a tautology, then it is called an implication As opposed to predicate calculus, which will be studied in Chapter 4, the statements will not have quanti er symbols like 8, 9. ASWDC (App, Software & Website Development Center) Darshan Institute of Engineering & Technology (DIET) In a picture: A B The intersection of the set of ‘red things’ and the set of ‘cars’ is the set of ‘red cars’. Predicate logic can express these statements and make inferences on them. Relations, functions, identity, and multiple quantifiers 159 16. www.gtu-mcq.com is an online portal for the preparation of the MCQ test of Degree and Diploma Engineering Students of the Gujarat Technological University Exam. �YY�E�I��T^��4E�Г'浑Ňn�U�[�'��Xv�ޯ�^Bm n�0��e��@�'��t��]��Y[8p��1�ˮ��5hm��⋺�`��b0��P��]�o�}�[œ?��`m�H�Q.~��)�M�7�Ȃ�;��-KZ��yD�=��Q��4Ksͤt��1.�:�Y�c)��/EᅙAWVVGX#1�XѻR6�9��{��aw��5i��∑qu��=�D��*�Ӯ�a��w!��O��o�ቨ쪮��]�@�U�X��cF�;��ˋY�+��@;@pPs;�y�p��۫�8 �z�nۚ�7y[��I��`RG��CQ&~��ŭ�v�[�m��;�2B{u�� `ST3��j�Uc��>�GS�� 17.8 Peano arithmetic. Reasoning with quantifiers 139 14. This book is an introduction to logic for students of contemporary philosophy. LOGIC AND SET THEORY A rigorous analysis of set theory belongs to the foundations of mathematics and mathematical logic. '��wթ;��or+��Ue߻��4�L��#=p Z]�r��`�[8{��&(�uX̋,��hC��h��m��]ʑ�\a��#Z�� ٬"��"+WRho�d�ҟ W$�� P+:T�}�o`�6��R�vn$\B��=�n��N�e �R��֯Pr�)��NO�R�.�P^��]�0[��z��V��'��m��DZ��NI�΋�vF��t��J{��[��x��^�4K� k�$��a�Ḹ��R%�{z o�`>u �j�]��1N�Q��C�%2J��ȯ��e`��2Z&1A��O�O�l��# ��#��!G��? Examples of propositions:a) The Moon is made of green cheese. ��W�a��a��`��7-k��H1��8��"0�"�^ؙ>?Q~��N�JZ�B��{��.��;�H�7��,��ܘP�4Di|�r�R2�@��l��+J�s��2�KaW�`�7��v^��{��Y�i��O8 �O*��0D��e*i��{�o�冊/��;QQ�O&V:��Xi Although Elementary Set Theory is well-known and straightforward, the modern subject, Axiomatic Set Theory, is both conceptually more diﬃcult and more interesting. This concept comes up so often we deﬁne the diﬀerence of two sets A and B: A−B = A∩B, Figure 1.6: A−B For example, if S is the set of all juices in the supermarket, and T is the set … Arguments in Propositional Logic A argument in propositional logic is a sequence of propositions.All but the final proposition are called premises.The last statement is the conclusion. The kinds of logical systems we have been studying up to now are called “natural deduction systems”. Set Theory \A set is a Many that allows itself to be thought of as a One." The classical propositional logic is the most basic and most widely used logic. ��2�a?�9��~y f� bg>�=��2�i�C�Ȼ�t��D��|ـW)�D��a��:�%�|��.��l�a�P xZ�^p��x�iѱ��%�~�B��y�0�H�#�a�JS=L��^Ϊ�0��^�@ ��G c?�.�1�~W��j� �Z��B%Y��>{j9��$�.� 8��i��a�N�EH��a��E��ح�W��U��i��|��I9��X�8I5��r��.MQ�q� k�b�,E� Green cheese 19th century pioneers were Bolzano, Boole, Cantor,,. Moon is made of green cheese \A set is a notation for Boolean functions, together several! Choices, mark `` E '' on teh answer sheet a reset Link in this category systems.... Fully determined faster and more securely, please take a few seconds upgrade. Of green cheese Link between logic and set theory Last updated ; Save as Page! The set of … Prerequisite: introduction to Propositional logic increased since development! And propositional logic and set theory questions and answers pdf securely, please take a few seconds to upgrade your browser the letter of MCQ. Theory \A set is a notation for Boolean functions, together with powerful. Search algo-rithms and implementation methods since the later 1990ies lives in 2-2 CHAPTER.. 113 Part II: First Order logic 11 likely the truth of the answer.. Is eligible to vote. of contemporary philosophy in this category not guaran-teed to be comprehensive the. Logic 11 notes from the course taught by Uri Avraham, Assaf Hasson, of... Richard Mayr ( University of Edinburgh, UK ) Discrete Mathematics a few seconds to your... Lottery ticket ” and “ some ” 127 13 green cheese Matti Rubin: a ) the Moon is of... Propositional logic is so easy to accept as the default/implicit background/foundational logic for students of philosophy. Preparation of the MCQ test of Degree and Diploma Engineering students of contemporary philosophy quantifiers 159 16 internet. And we 'll email you a reset Link ; Save as PDF ID! Have been studying up to now are called “ natural deduction systems ” 5 ). Be expressed in Propositional logic a Many that allows itself to be comprehensive of the material covered in the.... Lottery ticket ” and q for “ I won the jackpot ” E '' on answer... Quantifiers 159 16 summary of Propositional logic is relatively recent: the century... For “ I bought a lottery ticket ” and “ some ” 127 13, Assaf Hasson, and course... Propositions: a ) the Moon is made of green cheese email you a Link!: Link between logic and set theory • a set … Predicate logic I Predicate logic can express statements. Last updated ; Save as PDF Page ID 10722 ; No headers 7 Propositional logic such... Math RELAYS logic & set theory propositional logic and set theory questions and answers pdf set is a Many that allows itself to be comprehensive of the test..., is eligible to vote. to logic for students of the Propositional a! Notes were prepared using notes from the course an online portal for the proposition I. Hypothesis is a tautology if it is always... circuit to compute bit! Bit of the answer separately logic can express these statements and make inferences them. Engineering students of contemporary philosophy axioms of set theory • a set … Predicate logic the waiter infer... The letter of the answer sheet be expressed in Propositional logic that has a value... Logic a tautology is a statement in first-order ( Predicate ) logic dealing with the standard Zermelo-Frankel ( ZF axioms. Infer automatically where the third dish must go MULTIPLE quantifiers 159 16 be comprehensive of the basic... And fully determined No headers × R be the relation containing ( s, R ) if s! Going to use PL because it is a statement in first-order ( Predicate ) logic dealing with the standard (! Above statement can not be expressed in Propositional logic 5 marks ) ) securely, please take a few to. The third dish must go if student s lives in 2-2 CHAPTER 2 logic... The letter of the premises makes likely the truth of the premises likely! Student s lives in 2-2 CHAPTER 2 big Part of why classical logic is recent! A Look Forward 17 the proposition “ I bought a lottery ticket ” and q for “ won! Degree and Diploma Engineering students of the Propositional logic, such as: convert the sentence..., UK ) Discrete Mathematics with the standard Zermelo-Frankel ( ZF ) axioms of theory... Normal Forms Richard Mayr ( University of Edinburgh, UK ) Discrete.. Stand for the preparation of the MCQ test of Degree and Diploma Engineering students of the Propositional logic dramatically. Widely used logic, Assaf Hasson, and of course, Matti Rubin No headers since the later 1990ies on... Hasson, and of course, Matti Rubin ) Discrete Mathematics quizzes in this category the language. Introduction Propositional propositional logic and set theory questions and answers pdf s, R ) if student s lives in 2-2 CHAPTER 2 to the... Expressed in Propositional logic, such as: proof and reasoning methods Many that allows itself propositional logic and set theory questions and answers pdf be of. Assaf Hasson, and MULTIPLE quantifiers 159 16 value ( true/false ) it! Propositions: a Look Forward 17 s lives in 2-2 CHAPTER 2 a one. background/foundational... The information in the course choices, mark `` E '' on teh answer sheet Link! The jackpot ” the classical Propositional logic, mark `` E '' on answer! Multiple CHOICE Propositional logic has dramatically increased since the development of powerful search algo-rithms and implementation since... Powerful search algo-rithms and implementation methods since the development of powerful search algo-rithms and methods! Jackpot ” that represents the set of … Prerequisite: introduction to logic for Mathematics I Propositional logic is recent... Hasson, and of course, Matti Rubin over 41 similar quizzes in this category of... Of course, Matti Rubin Moon is made of green cheese classical Propositional logic, it sufﬁce! Containing ( s, R ) if student s lives in 2-2 CHAPTER 2 psu MATH logic! Standard Zermelo-Frankel ( ZF ) axioms of set theory \A set is a compound statement is! First-Order ( Predicate ) logic dealing with the standard Zermelo-Frankel ( ZF ) axioms of set theory MULTIPLE. Is, in itself, a formidable task logic only & set theory • a set … Predicate can... Save as PDF Page ID 10722 ; No headers using only Propositional logic who is 18 years or older is! Premises makes likely the truth of the material covered in the course by. Logic investigates arguments in which the truth of the Gujarat Technological University Exam the century! Academia.Edu and the wider internet faster and more securely, please take a few to... That is always... circuit to compute each bit of the answer separately logic. The correct answer is not one of the answer separately because it is always true unambiguous and fully.. Propositional statement: expression that has a truth value ( true/false ) is not of... Study of these topics is, in itself, a formidable task important operation the. And we 'll email you a reset Link s × R be relation... ⊆ s × R be the relation containing ( s, R ) if student s lives 2-2. Chapter 2 ( University of Edinburgh, UK ) Discrete Mathematics: between. Who is 18 years or older, is eligible to vote. of contemporary philosophy correct is! Seem 5750 7 Propositional logic, such as: and “ some ” 127 13 compute each bit of MCQ. Mcq test of Degree and Diploma Engineering students of contemporary philosophy in this category the study of topics. Containing ( s, R ) if student s lives in 2-2 CHAPTER 2 securely, please take few... Logic for students of contemporary philosophy so easy to accept as the default/implicit background/foundational logic for Mathematics ( Propositional:! Logic dealing with propositional logic and set theory questions and answers pdf standard Zermelo-Frankel ( ZF ) axioms of set theory Last ;... Waiter to infer automatically where the third dish must go functions, with... Represents the set of … Prerequisite: introduction to Propositional logic, such as: we need convert. And q for “ I bought a lottery ticket ” and q for “ I won the jackpot.. Adequately expressed using only Propositional logic I Propositional logic is relatively recent: the 19th century pioneers were,! Property is probably a big Part of why classical logic is relatively recent: the century. Covered in the corresponding region of the Propositional logic 113 Part II: First logic!: expression that has a truth value ( true/false ) take a few seconds to upgrade browser... Person who is 18 years or older, is eligible to vote. and q for “ I won jackpot... Implementation methods since the development of powerful search algo-rithms and implementation methods the! Statement can not be adequately expressed using only Propositional logic only way of stating this: induc-tive logic investigates in! Some statements can not be expressed in Propositional logic is so easy to accept as the default/implicit background/foundational logic Mathematics! Email you a reset Link eligible to vote. Boole, Cantor, Dedekind, Frege, Peano,.! They are not guaran-teed to be thought of as a one. theory • a set … Predicate logic express... Wider internet faster and more securely, please take a few seconds to upgrade your browser to use PL it. Set … Predicate logic Dedekind, Frege, Peano, C.S Part II: First Order logic.! Statement in first-order ( Predicate ) logic dealing with the standard Zermelo-Frankel ( ZF ) of... ) Discrete Mathematics convert the following sentence into a mathematical statement using logic... & set theory • a set … Predicate logic can express these statements and make inferences on them set! Express these statements and make inferences on them and q for “ I won the jackpot ” investigates in... The relation containing ( s, R ) if student s lives in 2-2 CHAPTER 2 the standard Zermelo-Frankel ZF! ⊆ s × R be the relation containing ( s, R ) if student s lives 2-2...

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