universal and existential quantifiers examples pdf
0000007672 00000 n �4(��qt���r,0�sX�7N�=H: ?������h�TՔ�>U�Q 8�dS��a JWW\Ռ���A�:�[email protected]��,���Hky]Щ=�Z��7:͓e���}#�@��☮-��A�gy� 8�#j�,W�^����@��Yk&�&2�N�^apA�g�^f�fh�f�a�f�y�����BW��i1�h��.�����@$�"�k�5�.� �bp�kC�ig���uޑn4�1њ�6f��A>OɆĕQ�r�dڤZ���9�tR�\M7&�hAŹV(�cʖn�h䮶��������P�k�[email protected]@��Y����,����a�����,B�T���Ņ�끟���/ �; j endstream endobj 10 0 obj 887 endobj 4 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F1 6 0 R /F2 7 0 R /F3 8 0 R >> /ProcSet 2 0 R >> /Contents 9 0 R >> endobj 13 0 obj << /Length 14 0 R /Filter /LZWDecode >> stream �y.�����u��WT 7Mc��=�R(6���+��%�sL>�Z�4g��3 Tv ��k�!�D��2dH|��OL�Dg���d� U����y0��F'C���t��DR;,������� �y����� �s���)d�0w�|�E3ŧy;���L�q�����Y�h�H_h�����Kjx����b���x �kF��w��D�2bi��ڟ�^q��8b��4��9p��ի�Q�橻ȁ�Z����y�X���?��]a���BC�����Y�^�t��̪��N�t��֩�aH>���@ ���2~7�@ѡ޳/4���7(�y�=E'˄O^���u�R�̃i�S�w�ytv06����ް�;��j����Ǿ�ϰTyQҰ�����gs n&�:�u��VB�����? 1 0 obj 0000003004 00000 n For example: if n = 1, we obtain the proposition: 1 is an odd integer (True). 0000004366 00000 n c�* endstream endobj 71 0 obj 569 endobj 72 0 obj << /Filter /FlateDecode /Length 71 0 R >> stream 0000003988 00000 n If n= 2, we obtain the proposition 2 is an odd integer (False) A propositional function is true or false of an individual. Universal Quantifier Existential Quantifier Mixing Quantifiers Binding Variables Negation Logic Programming Transcribing English into Logic Further Examples & Exercises Quantifiers Introduction A predicate becomes a proposition when we assign it fixed values. 2. �P&��". Example Every monkey has a tail x y P(x,y) y x P(x,y) m t has(m,t) Everybody loves somebody vs. 0000008950 00000 n %PDF-1.1 %���� 9 0 obj << /Length 10 0 R /Filter /LZWDecode >> stream 0000010208 00000 n G���$t��C�:��#��Բ��[�Ū5��:�Or�"�LZ%���,�c�ӻ�T��{$z�e��_�k�:�u|��� �Ȥd�� ��M#����CC#@JJJ*[email protected][email protected] ��..��� (�Q� 0000001862 00000 n '��j昉��ru�-����R�!����� 0000001634 00000 n %PDF-1.2 %���� <> Quantifiers • Universal P(x) is true for every x in the universe of discourse. 4 0 obj Someone is loved by everyone t m has(m,t) Every monkey shares a tail! 0000007693 00000 n In Fact, there is no limitation on the number of different quantifiers that can be defined, such as “exactly two”, “there are no more than three”, “there are at least 10”, and so on. endobj 0000010229 00000 n 0000007169 00000 n 0000002057 00000 n stream 0000005854 00000 n 0000001087 00000 n 0000003192 00000 n 0000006312 00000 n 0000006291 00000 n endobj <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 576 756] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Universal elimination This rule is sometimes called universal instantiation. ?�r��W(����8Fa2|f�H�;w�S�\2Ic2=�eH�_�#��'��0v����t���t�?��r=��Q��ׅ�[email protected]�vL����'*�V+:�����>@.22.�#��e*�$7��>0-�TYMx����y�a�/ۥ�(�Fv ����:�! 0000004186 00000 n �AP`5F�q���@("Nf3���eL'CA��34��b���2�c1�!RF(1g��ޅ�EC���NS2�Ά�y�.���ј�2-�T#��ʫF��M�A$�sNd�q]� �[�q��m� �PK2����@��o9�lV���V 3 0 obj A simple Aristotelian form Consider a slight variation on an example we looked at above: Every cube is left of a tetrahedron. After x is set, we can find at AT LEAST ONE y based on x such that x +y = 4. 0000010891 00000 n Chapter 12: Methods of Proof for Quantifiers § 12.1 Valid quantifier steps The two simplest rules are the elimination rule for the universal quantifier and the introduction rule for the existential quantifier. 0000001655 00000 n 0000009558 00000 n H�|SMs� �^�+�f"�B����g����c5Xx$9����ӷ=�^lo�}˾hC|+?��,#�rR��s�ܩ��}Qak��?Tp�Ӗ��-1Пŏ��E��b��I�s�P. For example: p(x): x is in Texas, D= set of cities and towns in the US. 0000005058 00000 n ��� 4�T��� �T3G#p�@5 H�lSMo�0��+�hK��1`��H�*Ej�K�6�"��l�������BZUHx̌߼�$=>(����RP?&�+[@k}��&���6�BJM%m��PP? 0000008325 00000 n �*��DE��`�h7�C����r�1�X��h�;D� -����~��.WB���[3L�)��E�3���gU�KA�h/hA����� ��،N+� �Q�� �;"�+�����{�8Cx�� *� �J��mJ~�3Т(���B���β��r�$�0�76�.�5����8b߳�p�9E)��G(�e#�l>�)2��f2��0�>�k���`��@Dpx�����4',�Ʈ��ү��4�#�,7A��1�R>ߨ�,��K Ĭ��ja4ij[email protected]��i��;:c�A%P��.�����C|f2F��t"�JO <>>> Examples • ‘For all x ∈ R, there exists y ∈ R such that x+ y = 4.’ This statement says that the following in this exact order: 1. 0000002451 00000 n 0000008929 00000 n 0000003383 00000 n trailer << /Size 95 /Info 56 0 R /Root 59 0 R /Prev 36892 /ID[] >> startxref 0 %%EOF 59 0 obj << /Type /Catalog /Pages 57 0 R /Outlines 29 0 R /OpenAction [ 60 0 R /XYZ null null null ] /PageMode /UseNone /PageLabels << /Nums [ 0 << /S /D >> ] >> >> endobj 93 0 obj << /S 223 /O 305 /Filter /FlateDecode /Length 94 0 R >> stream

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