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a1soln - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER...

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CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE & SOFTWARE ENGINEERING COMP 232/2 Mathematics for Computer Science FALL 2010 Assignment 1 Solutions 1. In each of the three cases A is a knight and B is a knight , A is a knight and B is a knave , A is a knave and B is a knave , A would have answered “yes”, and in the case A is a knave and B is a knight A would have answered “no”. Since A’s answer determines the status of A and B uniquely, A’s answer must have beeen “no”, and it follows that A is a knave and B is a knight. 2. a) Tautology b) Contingency c) Contingency 3. a) ( ¬ p F ) p ( ¬¬ p F ) p ( p F ) p p p ≡ ¬ p p T b) ( p q ) ( ¬ p r ) ( q r ) ≡ ¬ ( ( p q ) ( ¬ p r ) ) ( q r ) ≡ ¬ ( p q ) ∨ ¬ ( ¬ p r ) ( q r ) ( ¬ p ∧ ¬ q ) ( ¬¬ p ∧ ¬ r ) ( q r ) ( ¬ p ∧ ¬ q ) ( p ∧ ¬ r ) ( q r ) ( ( ¬ p ∧ ¬ q ) q ) ( ( p ∧ ¬ r ) r ) ≡ ¬ p q p r ( ¬ p p ) ( q r ) T ( q r
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