Translating into propositional logic a: you are a computer science major b: you are a freshman C: you can access the Internet from campus you can access the Internet from campus only if you are a computer science major or you are not a freshman, c →a V ¬b . A set of sentences defining a set of vectors is called the axiomatization of the set of vectors. ]"��N!��^V'�r+�LN�]���i,�ʯg�_�``�d��c�6��%vܡ��~���Y�X��͂�Q��y+(g�j .��yںr�Ε�1[���RA�U�O�V�y�@�c� %PDF-1.5 We have to consider the … ! ��eT��f�ZH- �F�Lr#�� p�EZm��� m�$7Ҟ 7�MT��f�ZH- �F0����b 8�� Math 127: Propositional Logic Mary Radcli e 1 What is a proposition? If I(p i) = 0, then p i is called false under the interpretation I. G��jOuO~9(�È�=i�i� ����=G���V�M�Y~��+�K�&a�*>�G���B�� �(1�ﴸH������edf�0��Oc���'47�m� I ��4B���d+{14[t�JK_�.��+Ū��=��^H0��pB�&I�l��!�](��[��9[v����.0�ǽ ��|>�}^��� 3��%=_f���_���l[��OOZ��ő���~xR ��Qc��_K)�1c��&����pv��~E���=Ȓ+�\�xpM�� ����w��|q���la> ����2J���'����6��~Ͱ5tdi�K��_�!Y�r���Q�,�����Д��#�� ��K�t�}��$c�e}u� &��o�e~���?����k#���f"��7� �rRr��R!�Iw�"JWT*V��3�0Ҏx�f�� {��l�[���K�`�R���*R��`$��j�;.�&���q�����Q٘����*琂��ɐ_Qj�U9f����I�Zli}� Z��z�S�yO� �x"tb�v�v�X3���M"�B�_��,l��ts�Dž-ӠʍƂ�T���eIR���4\m����@�A#�Ԗ�k0A����HD$���9����!zg����-Q8�����}�4�����ە�ڰ{=f.�Oa{>3�sZ�l�7d���H���$�`V�����S�aKl��nW�:�K�,�l�w��-V��P�|�yI��u� �P�z�D(�W�-�HD�c#��,E�@�V�V�������nA:al�7�BP��b���0�/��՟���"�t�/ ��l��n����[�a�\�$ڮ�L�m�H���nL1і��q�Y�]^��$g�5�\+����6��T]f�-�Y����6ռ#�NT��uը���F�$��3��D����a k�� �z� ;��R�. �6��Bj�6���i��k��Th��R �̈́�H{: 6�B�B�� ��Z ��h&�G����z:Zm��� mD3ᅑ�� �. PROPOSITIONAL FORMULAS: SYNTAX VL Logic Part I: Propositional Logic. ��~ߥ�[�Iq�6�}.uQ�I,�d���0�LS�h�bu��ܨ����l=Ų�(�y�Y鲖����얒�x�tɪ� �e����x�Q6��7����#u���q�DJ�v>��rl���LϦȡ�����Ͳi)c{��@qXaֽ� iqJ/��&w���� 4nA��^�NQ�t���b����7�NiE.l3�I!u�)d����^��p+'�j)t�w�c&�^]a{�Ŧ�w�#����K�?ۥ�+�L�/�Hߜ�������l�Y0�1���e��N��TO��-#4�rl�E�;�а�D�eX�*�JyU���6�~Q��z����. All men are mortal. 5 0 obj K�$�`9���PB�����{.q9"����m���7�ۉ]o����r�Ė4?&� ��X��k0��"{�0�%� ! Variables (x,y) can take arbitrary values from some domain. note formulas of propositional logic. Axiomatizability. Propositional Logic In this chapter, we introduce propositional logic, an algebra whose original purpose, dating back to Aristotle, was to model reasoning. %�쏢 G�i�7ه ȗI�,�5$b��“�Y��2UE�EK�L(/P�����G��c�$���To)�~=�X��ߜČ�@ǖ:�6�=u���R��ti�.#�J|���9�Z&�n����04-S1^$��7�ً�������*�|�i ����h2�xW�ԙwW����O��R�)��09�M:� ��&�o� ���h���ƁS$y�*k����j�U�)���Ԫi7MY���?v�q�$U2��U�K��6��G b��k��zj�ʒv��X�9�iy�����ws�7�)�,����|���]�2��ގNpN� �[U�����s܂ᴅ��R���_`���n���LWK���~�q�j��s�u��q����VFӜ�t� x��ً��0�������>�%�3%�$�}�� �C��ݑ� �t��j3 �� h#h&��� �n��j3 �� h#h&ё� ��5Th��R �̈́���7��^L�B�� ��Z ��h&�x�= ��\zZm��� mD3�7#�e ��T��f�ZH- �F�Lr#�q p%]IZm��� m�$7�� '҉T��f�ZH- �F�L�#� pGZm��� m�$7� & '�� jt9�%�V� ��C����� Statements in Predicate Logic P(x,y) ! 1�X��*oS�t~�f �΂�� md��TC(���T��g MpÓaԍ��������W&D�M�/�s��g2�,�l��z�'=�情q��,r��t�$d努~��jJHN"������/���=a,)���!`}V���u�DfU�ZN]5 propositional logic, such as: ! [������΃��O�v��^�MR�Q� �쥊va�E� Example: Party Planning We want to plan a party. In order to consider and prove mathematical statements, we rst turn our attention to understanding the structure of these statements, how to manipulate them, and how to know if they are true. ����� #�|Q=�H��l��h��B:��������̗�"-��Xk�-m�r�ot��]��. {iFm�ڟ���/˽���1�]Tct������j�93|~8�R 12 0 obj <> /XObject <> /ProcSet [/PDF /Text /ImageC ] >> /Group 14 0 R /Trans <> /Parent 22 0 R /MediaBox [0 0 453.543 255.118 ] /TrimBox [0 0 453.543 255.118 ] /Rotate 0 >> endobj 2 0 obj <<>> endobj The fundamentals of proofs are based in an understanding of logic. Logic in Computer Science 4. ��n}\G2��y�K]����ҚȲ޻�u�#U�$ R�u�TzŴ7��e|e����OXY�����Չ�&x�'����{�ܚ���-� ��M9ɇ�K�T�Ӂspi�R2#������H#�!p;��Y�揚܍��J,ͻ����t���$s��6��3�u�o�&m���.���kl�=��L�HcӉW>sG"�G'�!��i���t;�v�s�M�ID�ϐ�3���^f��"9�ܨɊ�]U/��-��z�_K�|�y�l�4i�4ק��s��B�2�H7�G5��D��ST��v�s��� ����J)��s)$9�����¾;v�|�-V,�m_LG��xM����}�z9YT�h+�fb��T�}4�l9��e�A�=S� ! propositional logic if and only if there is a signature of size n and a set of sentences from the corresponding language such that the vectors in the set correspond to the set of interpretations satisfying the sentences.

propositional logic pdf

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