/A << /S /GoTo /D (subsection.5.6) >> /Rect [466.521 182.413 478.476 190.826] /Rect [466.521 230.234 478.476 238.647] /Subtype /Link /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /A << /S /GoTo /D (subsection.3.1) >> /Subtype /Link QUELQUES EXERCICES CORRIGÉS DE DÉDUCTION NATURELLE. /Type /Annot /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] 126 0 obj << /Border[0 0 0]/H/I/C[1 0 0] �U�Q._6Vۚ��B�������:`Ѿ&���bQMԬ`�/�*,���_EVw9Q��{l��͙\���#�H�D��H.��Ů{ߛ���A�\G�����9+�R�" 149 0 obj << << /S /GoTo /D (subsection.4.6) >> 101 0 obj /A << /S /GoTo /D (subsection.4.5) >> /Rect [132.772 495.295 227.233 506.144] /Rect [147.716 309.99 258.246 320.838] /Subtype /Link (Biconditional) /Border[0 0 0]/H/I/C[1 0 0] B��[;��Oׂ�K�{=�U�=�5��I�'��fEY�@�{�N�_��;�M���^���)Ov�fw|���T����&�dtycK6bk��p�ƫ�]�8+RS����R7���a�ip:�'�Eb�)�O�"��"��"k:Jq��J�b~f��-|�����L�����ڌ���@�@� (���! >> endobj 57 0 obj /A << /S /GoTo /D (subsection.3.2) >> 167 0 obj << 49 0 obj /Type /Annot 20 0 obj 131 0 obj << endobj 153 0 obj << endobj (Disjunction) endobj /A << /S /GoTo /D (section.2) >> 155 0 obj << /Type /Annot /Subtype /Link >> endobj (Implication) << /S /GoTo /D (subsection.5.2) >> 159 0 obj << /Border[0 0 0]/H/I/C[1 0 0] >> endobj /Border[0 0 0]/H/I/C[1 0 0] endobj 132 0 obj << >> endobj xڕYYs�~�_1o��V\������Q��I�*r��f�DrB��U~}���u^�@�4}|�Iv�]����D���{��&�wJǙ.����NeY\ծ��8�����o���V*ͣ��k�W�Y�G��yn]��*S�����~����q]����SW��U�hJ�3��V0�z����4��2�x���4��ނ�H�~p]++��}c��=t�4r-�;��`�0t���OY�>��k��,K���J�u��a���臫\E�ݞI4����@Uƥ�`%Z��{�U��ʢ�yD�푦�ߙ�5SF��꺪+ٳ��޾��G�뙆�"e�J�ۃh D�]����H%��cZ���[���G��%pMo::.6N����*�����9�]�eV!CWe /Rect [147.716 345.856 222.63 356.593] /Type /Annot >> stream /Border[0 0 0]/H/I/C[1 0 0] /A << /S /GoTo /D (subsection.5.2) >> >> endobj 11 This one seems easy. 173 0 obj << 40 0 obj /Border[0 0 0]/H/I/C[1 0 0] 154 0 obj << /Type /Annot 3 0 obj << >> endobj /Subtype /Link /Type /Annot (Universal quantifier) /MediaBox [0 0 612 792] endobj endobj /Border[0 0 0]/H/I/C[1 0 0] 127 0 obj << /A << /S /GoTo /D (subsection.5.6) >> /Subtype /Link 5. << /S /GoTo /D (subsection.4.9) >> 5. >> endobj (Practice problems) 156 0 obj << 115 0 obj << /Filter /FlateDecode /Rect [466.521 299.972 478.476 308.385] endobj /Border[0 0 0]/H/I/C[1 0 0] endobj >> endobj 108 0 obj 145 0 obj << /Type /Annot /Subtype /Link << /S /GoTo /D (section.1) >> /Subtype /Link 185 0 obj << /Border[0 0 0]/H/I/C[1 0 0] endobj /Border[0 0 0]/H/I/C[1 0 0] >> endobj /A << /S /GoTo /D (subsection.5.4) >> (Identity) /Type /Annot /Contents 172 0 R /Type /Annot endobj 5. 140 0 obj << 7 One with proof by cases. /Rect [466.521 347.793 478.476 356.206] >> endobj /Font << /F15 175 0 R /F16 176 0 R /F35 178 0 R /F36 179 0 R /F8 180 0 R >> (Conjunction) << /S /GoTo /D (subsection.4.8) >> >> endobj /A << /S /GoTo /D (subsection.4.10) >> L2 7 calcul classique des propositions est dit "monotone" en vertu de cette propriété. >> endobj /Subtype /Link /Type /Annot /Type /Annot 93 0 obj 113 0 obj endobj 53 0 obj /A << /S /GoTo /D (section.5) >> /A << /S /GoTo /D (section.4) >> 37 0 obj x��Ks�0���:�TZ�:��ig��L��!��ġ�#��|�J;1���L�p���CZ�Ȑ0�q��z{N�$LFJ�e$4�ހ\��U��=Mg�"�G�`ޟ�Ӊ�y��i?��^?z��aE8���` +i@B%�;������ya,���iQؑ#�cs�����KZT��ܭ�x�D�yz��J$�hQ�!�,q��3 5. /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot endobj /Type /Annot 174 0 obj << /A << /S /GoTo /D (subsection.5.9) >> >> endobj /Rect [466.521 335.838 478.476 344.251] �/7t��|���iq甦�N�����UD`"��JD8�o�VtZ\ۇ�N#�M�7e�J�\{��I��xC��s}-���OF%�Uج�2 �4 48 0 obj /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot 162 0 obj << /Rect [466.521 371.703 478.476 380.116] /Subtype /Link << /S /GoTo /D (subsection.4.1) >> /A << /S /GoTo /D (subsection.5.3) >> 24 0 obj -�oW���J8�����Yl%��h�5N�N���5i����m�|?�w��(!�_HB�QXH��!��aK�B!�@d�$���?�Iï�|��c�qH+��4A0"�/! >> endobj /A << /S /GoTo /D (subsection.4.5) >> endobj endobj /Rect [147.716 357.811 222.159 368.659] 88 0 obj /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot /Rect [147.716 369.766 226.034 380.504] /Subtype /Link endobj 138 0 obj << 5. 73 0 obj endobj endobj @�@��e[� /Rect [466.521 158.503 478.476 166.916] << /S /GoTo /D (subsection.5.3) >> >> endobj /A << /S /GoTo /D (subsection.5.8) >> /Rect [147.716 180.476 211.643 191.213] endstream 114 0 obj << /Subtype /Link /Type /Annot /D [114 0 R /XYZ 133.768 538.079 null] 128 0 obj << 1 0 obj /D [114 0 R /XYZ 132.768 705.06 null] /Border[0 0 0]/H/I/C[1 0 0] ��X-���ިT�QE��FR ���h�9Z��?�a8���X�D������;�*�i���$�0�DI�]�@��j�����̄U���J /Subtype /Link 61 0 obj (Summary of rules) /D [114 0 R /XYZ 133.768 667.198 null] /Type /Annot /Subtype /Link /Rect [466.521 194.368 478.476 202.781] The pack hopefully o ers more questions to practice with than any student should need, but the sheer number of problems in the pack can be daunting. /Rect [465.026 254.144 478.476 262.557] 150 0 obj << /Type /Annot >> 89 0 obj 120 0 obj << /A << /S /GoTo /D (subsection.5.7) >> /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link 143 0 obj << /Type /Annot 17 0 obj >> endobj /Subtype /Link /Subtype /Link /Type /Annot 5. /A << /S /GoTo /D (subsection.3.2) >> /Rect [147.716 321.945 211.643 332.683] /Type /Annot 77 0 obj endobj endobj 165 0 obj << /Subtype /Link endobj << /S /GoTo /D (subsection.5.7) >> 36 0 obj endobj endobj /Border[0 0 0]/H/I/C[1 0 0] >> endobj >> endobj /Subtype /Link 41 0 obj /A << /S /GoTo /D (subsection.3.3) >> x��XKo#E��W�hK;���~fh��!V����,@p@ ����yv�{<3�A��n�(�|�W�����zG� )���8��p(�S�� 0���o�_>m��W�By��~�}\.7���#��|x|��{&���v[� ��>m��W�����O�ۇ��X}{�/�;a�]@�+W=��w�;��+�kAN/ << /S /GoTo /D (subsection.4.5) >> /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] endobj /Border[0 0 0]/H/I/C[1 0 0] /A << /S /GoTo /D (subsection.5.4) >> << /S /GoTo /D (subsection.4.3) >> /A << /S /GoTo /D (subsection.3.1) >> /Filter /FlateDecode /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link 45 0 obj /A << /S /GoTo /D (subsection.4.2) >> /Border[0 0 0]/H/I/C[1 0 0] %PDF-1.5 >> endobj 5 Explained exercises. 1 A very simple one. /Type /Annot /Filter /FlateDecode 139 0 obj << 168 0 obj << Nvgr#�-��������\0J��Ƴ��M�Y&F. >> endobj /Subtype /Link >> endobj 72 0 obj endobj /Rect [466.521 170.458 478.476 178.871] endstream >> endobj /Subtype /Link << /S /GoTo /D (subsection.5.1) >> << /S /GoTo /D (section.3) >> /A << /S /GoTo /D (subsection.5.5) >> /Subtype /Link /Subtype /Link /Type /Annot /Rect [466.521 276.062 478.476 284.475] /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link (Identity) /Type /Annot 32 0 obj ����Q=��� �3 116 0 obj << endobj NZ �{��Z��٧1x���6�a|�%x����Tn /A << /S /GoTo /D (section.1) >> /Type /Annot /Type /Annot endobj /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot /Subtype /Link endobj /A << /S /GoTo /D (subsection.5.1) >> (Existential quantifier) /Subtype /Link endobj dX�trd'�tcg���h'��=�Ds�ǣwh��`P�ҹ��TT ,��N�*m"�o�Ҩg*�,��/o��-{����ҀVX���LNpƤ�]��E����;ʴ��]�]~�t�f�M~p�������������l"79(9^U���v!��L�j6��}���]z�����%��'d"�Q�Y`{�W*��7B��8 �7����o� ���~��5$�sZ�T�K �A�HF �33� /Type /Annot 129 0 obj << << /S /GoTo /D (subsection.5.5) >> /Border[0 0 0]/H/I/C[1 0 0] >> endobj endobj /A << /S /GoTo /D (subsection.4.7) >> stream << /S /GoTo /D (subsection.4.2) >> >> endobj (Universal quantifier) /A << /S /GoTo /D (subsection.4.3) >> /Rect [147.716 228.297 226.034 239.034] /Type /Annot (Negation) P��I�%P^WT�`d��xM�6�9l:���*�y-&=O�&��!�|�!õL N��cO(�Y�&� ��_ ��ܥ��n&߀p�R^O̙��=�q�ȕ@�gA[aT�ܙ��J 8j���Bq)���t���i�&(i&ѵ���R�����B�s�N��a5����](�/�K&}A��h&�}�z�4��VV��qa��3�=i0������D� 2�W� �2&K6G�5VV�j��K# ��&sn| ��X� /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link endobj >> endobj endobj *�ǭ�-or �?WƓ`7��6�8�e��h���:K$ ��>�� >> endobj /Rect [466.52 242.189 478.476 250.602] /Rect [147.716 415.594 264.169 426.442] /Rect [147.716 298.035 264.169 308.883] (Implication) 4 0 obj endobj 96 0 obj 56 0 obj /A << /S /GoTo /D (subsection.3.3) >> 12 An interesting one. >> endobj 5. /Rect [466.521 288.017 478.476 296.43] >> endobj endobj /Type /Annot 171 0 obj << /Parent 181 0 R
2020 natural deduction exercises