set theory and logic pdf

0000010201 00000 n 0000042018 00000 n țP� {�~حM�Ъ1��s,B��s�)Sd_�+d�K��|+wb�Lc�@Ԡ��s �r��@ံPv�⚝��s��; ��xBeY��^��cvhnϳ�y�W��`�9BD��#)p��a4S��RA��z�k�'y��~h�)�I��O��N�:+��*��ㄯ��y��mAu 9� &��7�^19�>� �%OD+U�|��F�~|I�n��;=��p��e��~ ,�/�� w��-�Ȼ�v|�2 zy?�tq~�iq�q��0��0q��h=�y�F_ A 0P�T��,��;@�ig�p��y�!��|n�v��P��b1%�� GLV.t�W[��Y�2��{N�Nw\=��Ԡ�2`q�#f��f��x�|X��|Z,�ns�f{��A��JU�en��ϛ��G�|��Eg-TX�2� ��"��0��=k3� �ʤu?-�P E��(��#�k��䐷��@�ˀ�A��a+��f�l2e��5��3�#�:�t2Tf�@xӄ�m2��DL��1M�1|3t��3�ї"r5��_%$�Qr��eZ��#�cr��˔��)l��m�Ӿ=��f��k8�B,ࡩ�m �uz��>��'GZBy��u8��?�Bx��["��CӴsd_T��T@0#�1�?��I~:c+�Yxrfl{��Ŝ #�r}�:�(��R=��KN�N�K]4��қ�p혉��a�]x�X�˽� ��v 0000065343 00000 n 0000041801 00000 n 0000038686 00000 n !��}�&)�MO8�eL6uFoJ��:�#@�f�� N`�`��RK��yD�}c~��'�*n��E��Ij�Tl Although Elementary Set Theory is well-known and straightforward, the modern subject, Axiomatic Set Theory, is both conceptually more diﬃcult and more interesting. 0000038078 00000 n 0000063492 00000 n 0000070198 00000 n V. Naïve Set Theory. 0000078112 00000 n Negation of Quantified Predicates. The subjects of register machines and random access machines have been dropped from Section 5.5 Chapter 5. Set Theory and Logic Supplementary Materials Math 103: Contemporary Mathematics with Applications A. Calini, E. Jurisich, S. Shields c 2008. /Length 2960 ��Xe�e�� 81��c�� ˷�孇f�0h_mw. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. %%EOF 0000003293 00000 n Proof by Counter Example. 0000056119 00000 n Universal and Existential Quantifiers. 0000069809 00000 n Clearly if a= cand b= dthen ha;bi= ffag;fa;bgg= ffcg;fc;dgg= hc;di 1. axiomatic set theory with urelements. 0000011807 00000 n Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. The empty set can be used to conveniently indicate that an equation has no solution. %PDF-1.2 0000047470 00000 n In mathematics, the notion of a set is a primitive notion. P!$� The major changes in this new edition are the following. x��A 0ð4�v\Gcw��z�C. 2. 0000073034 00000 n in set theory, one that is important for both mathematical and philosophical reasons. 0000064488 00000 n 0000041289 00000 n An appendix on second-order logic will give the reader an idea of the advantages and limitations of the systems of first-order logic used in 0000039153 00000 n 0000075927 00000 n File Name: Logic And Set Theory With Applications 6th Edition Pdf.pdf Size: 6514 KB Type: PDF, ePub, eBook Category: Book Uploaded: 2020 Nov 20, 04:15 Rating: 4.6/5 from 914 votes. trailer 0000047249 00000 n Chapter 1 Set Theory 1.1 Basic deﬁnitions and notation A set is a collection of objects. 0000021855 00000 n A. Hajnal & P. Hamburger, ‘Set Theory’, CUP 1999 (for cardinals and ordinals) 4. 0000079248 00000 n 0000011497 00000 n 0000070658 00000 n LOGIC AND SET THEORY A rigorous analysis of set theory belongs to the foundations of mathematics and mathematical logic. Basics of Set Theory and Logic S. F. Ellermeyer August 18, 2000 Set Theory Membership A setis a well-defined collection of objects. 0000041116 00000 n , 2. Set Theory and Logic is the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics.Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. In 1874 Cantor had shown that there is a one-to-one correspondence between the natural numbers and the algebraic numbers. %�� 1. 1592 0 obj<> endobj Methods of Proof. 14 Chapter 1 Sets and Probability Empty Set The empty set, written as /0or{}, is the set with no elements. Formal Proof. 0000039958 00000 n endstream endobj 1656 0 obj<>/W[1 1 1]/Type/XRef/Index[78 1514]>>stream Complex issues arise in Set Theory more than any other area of pure mathematics; in particular, Mathematical Logic is used in a fundamental way. 0000003046 00000 n Unique Existence. 1594 0 obj<>stream An Overview of Logic, Proofs, Set Theory, and Functions aBa Mbirika and Shanise Walker Contents 1 Numerical Sets and Other Preliminary Symbols3 2 Statements and Truth Tables5 3 Implications 9 4 Predicates and Quanti ers13 5 Writing Formal Proofs22 6 Mathematical Induction29 7 Quick Review of Set Theory & Set Theory Proofs33 0000001631 00000 n 0000045614 00000 n 0000063750 00000 n and most books of set theory contain im portant parts of mathe matical logic. 0000072804 00000 n Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. 0000039789 00000 n Mathematical Induction. LOGIC AND SET THEORY 1.2 Relations between Statements Strictly speaking, relations between statements are not formal statements them-selves. .6�⊫�Ţ1o�/A��F�\��6f=iE��i�K��Lٛ�[�n&]=�x�Wȥ��噅Ak5��z�I�� {]xKA}�a\0�;��O`�d�n��8n��%{׆P�;�PL�L>��бL�~ Primitive Concepts. Predicate Logic and Quantifiers. SECTION 1.4 ELEMENTARY OPERATIONS ON SETS 3 Proof. An example of an implication meta-statement is the observation that “if the statement ‘Robert gradu-ated from Texas … If the object x is a member of the set A, then we write x A which is read as “ x is a … For example {x|xis real and x2 =−1}= 0/ By the deﬁnition of subset, given any set A, we must have 0/ ⊆A. 2 0 obj Informal Proof. lX�Å 0000055776 00000 n 0000002534 00000 n 0000076098 00000 n /Filter /FlateDecode ��r��* ��/��8x�[a�G�:�ln-97ߨ�k�R�s'&�㕁8W)��+>v��;�-��9��d��S�Z��-�&j�br�YI% ��ZE$��։(8x^[��0`ll��JJJ...iii2@ 8�� Vfcc�q�(((�OR��544,#��\��-G�5�2��S�� |��Qq�M��l�M��(�0�)��@��!�E�ԗ�u��#�g�'� BLg�`�t�0�~��f'�q��L�6�1,Qc b�&``�(v�,� ��T��~�3ʛz��3�0{� p6ts��m�d��}"(�t��o�L��@��^�@� iQݿ ha;bi= ffag;fa;bgg Theorem 1.5. ha;bi= hc;dii a= cand b= d. Proof. III. 0000071716 00000 n %PDF-1.3 %�� De nition 1.7 (Ordered Pair). (Caution: sometimes ⊂ is used the way we are using ⊆.) Indirect Proof. 0000075834 00000 n 0000002654 00000 n IV. 0000022861 00000 n