natural deduction exercises

/Subtype /Link /Rect [466.52 242.189 478.476 250.602] 37 0 obj endobj /Type /Annot >> endobj (Using this pack) 7 One with proof by cases. endobj endobj >> endobj << /S /GoTo /D (subsection.5.8) >> /Rect [147.716 194.368 230.6 203.279] >> endobj stream /Subtype /Link >> endobj endobj /Border[0 0 0]/H/I/C[1 0 0] /Rect [471.502 417.531 478.476 425.944] /Rect [471.502 429.487 478.476 437.899] 137 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] /Filter /FlateDecode 120 0 obj << /Subtype /Link /Type /Annot 8 0 obj /Type /Annot << /S /GoTo /D [114 0 R /Fit] >> 125 0 obj << >> endobj /Type /Annot /D [114 0 R /XYZ 133.768 538.079 null] >> endobj /Border[0 0 0]/H/I/C[1 0 0] 149 0 obj << endobj /A << /S /GoTo /D (subsection.4.9) >> /Type /Annot endobj /Type /Annot /Rect [132.772 393.676 240.397 404.525] /Type /Annot /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] (Disjunction) 5. /Type /Annot << /S /GoTo /D (subsection.4.6) >> endobj /A << /S /GoTo /D (subsection.4.7) >> 52 0 obj /Border[0 0 0]/H/I/C[1 0 0] /Border[0 0 0]/H/I/C[1 0 0] endobj '*��a�`L�{��-S�0?8�É��iy�`��\��mKh��B'e�Z{�;А �A�D��ņ?Y 158 0 obj << /Subtype /Link 131 0 obj << 135 0 obj << /Border[0 0 0]/H/I/C[1 0 0] 132 0 obj << /Border[0 0 0]/H/I/C[1 0 0] 134 0 obj << /Border[0 0 0]/H/I/C[1 0 0] 89 0 obj endobj >> endobj >> endobj Ici, :C suitdesprémisses(1),(2)et(3);donc:Csuitaussidesprémisses(1),(2),(3)et(4). /A << /S /GoTo /D (subsection.4.3) >> 124 0 obj << /Type /Page /Rect [147.716 156.566 264.169 167.414] /Subtype /Link /A << /S /GoTo /D (subsection.5.7) >> /Border[0 0 0]/H/I/C[1 0 0] 36 0 obj >> endobj /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] /A << /S /GoTo /D (subsection.4.2) >> /Border[0 0 0]/H/I/C[1 0 0] << /S /GoTo /D (subsection.4.1) >> 5. >> endobj 64 0 obj 155 0 obj << 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. /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot 25 0 obj /Rect [147.716 439.505 222.159 450.353] /D [114 0 R /XYZ 133.768 667.198 null] 14 0 obj << endobj /Border[0 0 0]/H/I/C[1 0 0] i��q�c��\vM�psl8�yIx��pf� A�� b�(=��1��I��@�� *��:�f��ɷ(�D�F�"��U6�0d'��)��(.fp�l�hkۻ�4��0n��t��ue=��. 85 0 obj 5 Explained exercises. 21 0 obj 3 Starting to make suppositions. 57 0 obj /A << /S /GoTo /D (subsection.5.1) >> 45 0 obj /Subtype /Link /Rect [470.755 475.315 478.476 483.728] 122 0 obj << /Rect [466.521 335.838 478.476 344.251] 13 0 obj /A << /S /GoTo /D (subsection.5.8) >> 1 0 obj 5. >> endobj /Type /Annot endobj 163 0 obj << 61 0 obj 32 0 obj /Border[0 0 0]/H/I/C[1 0 0] 92 0 obj /Rect [147.716 242.189 193.129 250.989] /A << /S /GoTo /D (subsection.3.2) >> /Type /Annot 76 0 obj endobj 123 0 obj << %�� << /S /GoTo /D (subsection.4.5) >> << /S /GoTo /D (subsection.4.4) >> endobj 153 0 obj << 143 0 obj << %�� 164 0 obj << (Solutions) /Border[0 0 0]/H/I/C[1 0 0] 28 0 obj /Type /Annot /Rect [466.521 230.234 478.476 238.647] /Subtype /Link 49 0 obj /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot (Summary of rules) /A << /S /GoTo /D (section.3) >> 165 0 obj << /Border[0 0 0]/H/I/C[1 0 0] 41 0 obj /Border[0 0 0]/H/I/C[1 0 0] 96 0 obj 121 0 obj << /A << /S /GoTo /D (subsection.3.2) >> (Biconditional) 5 Reduction to the absurd. 8 One to think. 167 0 obj << /A << /S /GoTo /D (subsection.5.2) >> >> endobj /Type /Annot 142 0 obj << %PDF-1.5 /A << /S /GoTo /D (subsection.4.6) >> /Type /Annot /Type /Annot /Parent 181 0 R /Subtype /Link /Subtype /Link 69 0 obj /Rect [147.716 321.945 211.643 332.683] << /S /GoTo /D (subsection.4.9) >> endobj endobj >> endobj >> endobj endobj /Rect [465.026 254.144 478.476 262.557] 162 0 obj << >> endobj endobj endobj << /S /GoTo /D (subsection.4.3) >> /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot 5. >> endobj /A << /S /GoTo /D (subsection.3.1) >> -�oW��J8��Yl%��h�5N�N��5i��m�|?�w��(!�_HB�QXH��!��aK�B!�@d�$��?�Iï�|��c�qH+��4A0"�/! /Rect [147.716 309.99 258.246 320.838] /Type /Annot /A << /S /GoTo /D (subsection.4.6) >> 101 0 obj /Border[0 0 0]/H/I/C[1 0 0] endstream 138 0 obj << (Biconditional) 40 0 obj 118 0 obj << >> endobj /Type /Annot /Subtype /Link /Rect [147.716 228.297 226.034 239.034] /Subtype /Link /Annots [ 115 0 R 116 0 R 117 0 R 118 0 R 119 0 R 120 0 R 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R 129 0 R 130 0 R 131 0 R 132 0 R 133 0 R 134 0 R 135 0 R 136 0 R 137 0 R 138 0 R 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 144 0 R 145 0 R 146 0 R 147 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R 159 0 R 160 0 R 161 0 R 162 0 R 163 0 R 164 0 R 165 0 R 166 0 R 167 0 R 168 0 R 169 0 R 170 0 R ] /Rect [466.521 218.279 478.476 226.691] /A << /S /GoTo /D (subsection.5.2) >> x��YKo7��W�Qh��Hڴ*�('͡-�CѢ��ܧH��r��>Z�Ùo�p�9\��o % �P��PU~)ޯ��Vf��we�%��v��^��o@/��vͻ��{��E��ps]_]դ{w��Ï�^�,��Mo1B2b :��N�)W��. /Type /Annot /Subtype /Link Exercises to 1.8 Natural deduction. /Subtype /Link /Rect [466.521 323.883 478.476 332.295] 93 0 obj >> endobj /A << /S /GoTo /D (subsection.3.3) >> 114 0 obj << >> endobj >> endobj stream endobj /Type /Annot 140 0 obj << >> bĺ��^�LǺ�w�M��fY�كۛ��_�Jb�_I�DJ7E*_J�ۚ��l��'7��L�y��h� ��$�T�ˎ#��8E\�|��lFdq(�ǫ�w6W��wׯ�Dg��p�^��x��C�YV#=��l�&�,��C�ZXy��ƭzˬ��]M�;n=�9��=��4�ɜ/��`��箧x�2B�`��cbc�3�Ù�J�7�>)��Lʹ�N��#��6�O�γ�3Z�J�Ñ��tN�8F��C�iuH$��q3�1�0t�D�06�3st? /Rect [147.716 168.521 258.246 179.369] >> endobj (Additional challenges) /A << /S /GoTo /D (subsection.4.7) >> 113 0 obj 80 0 obj 105 0 obj 68 0 obj 5. /Subtype /Link >> endobj 12 0 obj 24 0 obj /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link /Rect [132.772 473.378 238.771 484.226] 60 0 obj (Negation) >> endobj /Rect [466.521 276.062 478.476 284.475] >> endobj 112 0 obj endobj 5. 144 0 obj << endobj /Border[0 0 0]/H/I/C[1 0 0] endobj 119 0 obj << /Border[0 0 0]/H/I/C[1 0 0] 117 0 obj << Ng�;�v䒁1��e-0�kL�z(B ��dh�AgWyiϐޘ��Zr*D endobj endobj endobj 3 0 obj << @�@��e[� /A << /S /GoTo /D (subsection.5.10) >> /Type /Annot /Type /Annot >> endobj 77 0 obj endobj (Additional challenges) >> endobj %PDF-1.5 /A << /S /GoTo /D (subsection.3.3) >> 177 0 obj << 13 I had this one in an exam. /A << /S /GoTo /D (subsection.4.8) >> /Subtype /Link >> endobj endobj << /S /GoTo /D (subsection.4.7) >> /Border[0 0 0]/H/I/C[1 0 0] (Existential quantifier) 185 0 obj << >> endobj endobj endobj endobj >> endobj /A << /S /GoTo /D (section.3) >> 104 0 obj /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] 1 A very simple one. endobj /A << /S /GoTo /D (subsection.5.5) >> endobj /Rect [466.521 170.458 478.476 178.871] >> endobj endobj >> endobj /Rect [132.772 495.295 227.233 506.144] L2 7 calcul classique des propositions est dit "monotone" en vertu de cette propriété. /Rect [132.772 254.144 195.6 263.055] 168 0 obj << << /S /GoTo /D (subsection.5.2) >> (Universal quantifier) >> endobj 154 0 obj << endobj /Subtype /Link endobj /Border[0 0 0]/H/I/C[1 0 0] /Type /Annot >> endobj /Type /Annot 150 0 obj << /Type /Annot /Rect [147.716 204.386 222.63 215.124] << /S /GoTo /D (subsection.4.2) >> >> endobj (Identity) /Rect [147.716 383.658 193.129 392.459] 173 0 obj << /Type /Annot 2�W� �2&K6G�5VV�j��K# ��&sn| ��X� /Border[0 0 0]/H/I/C[1 0 0] 1 (1) Use natural deduction to prove the following inferences: 1) 53 0 obj >> endobj 159 0 obj << /Type /Annot endobj 5. endobj /Rect [466.521 311.927 478.476 320.34] (Core) /A << /S /GoTo /D (subsection.5.9) >> 126 0 obj << /Rect [132.772 451.46 237.941 462.308] /Subtype /Link 5. /A << /S /GoTo /D (section.1) >> 72 0 obj /Subtype /Link /Border[0 0 0]/H/I/C[1 0 0] /Rect [147.716 144.61 206.939 155.459] /Border[0 0 0]/H/I/C[1 0 0] endobj >> endobj /Rect [147.716 427.549 258.246 438.398] /Border[0 0 0]/H/I/C[1 0 0] /A << /S /GoTo /D (subsection.5.9) >> (Universal quantifier) /Border[0 0 0]/H/I/C[1 0 0] /Subtype /Link /Type /Annot ��X-��ިT�QE��FR ��h�9Z��?�a8��X�D��;�*�i��$�0�DI�]�@��j��̄U��J /Border[0 0 0]/H/I/C[1 0 0] /Rect [471.502 441.442 478.476 449.855] endobj Exercices de déduction naturelle en logique propositionnelle Exo 1 Pour chaque séquent ci-dessous, s'il vous paraît sémantiquement correct, proposez une preuve en déduction naturelle à l'aide de FitchJS puis transcrivez la dans ce format (exemples).