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CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE & SOFTWARE ENGINEERING COMP 232/2 Mathematics for Computer Science FALL 2010 Tutorial Problems (Section DD) : Week 3 3-1. The logical operators ( nand ), ( nor ), and ( nimp ) are defined as follows. P Q P Q P Q P Q T T F F F T F T F T F T T F F F F T T F a) Assume $ is a binary logical operator, i.e. , one of the following. Show that ( p $ q ) ( q $ p ) T if and only if $ is the conditional operator. Hint: How are the truth tables of p $ q and q $ p related? b) Suppose F ( p, q ) is a logical expression involving only the propositional variables p and q . i) What can you conclude about F ( p, q ) if F ( p, q ) F ( q, p ) T ? ii) What can you conclude if F ( p, q ) F ( q, p ) T ? c) Write the following sentence (based on experiences driving on the Metropolitan Autoroute) in logical form. If the traffic stops moving I cry uncontrollably. Hint: This is an example of a statement in which “if” is used to mean “whenever”, so quantification must be involved. What is the domain of discourse?
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