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Unformatted text preview: p and q are false, and it is false otherwise. 1. Show that p q is logically equivalent to ( p q ). 2. If p p p and ( p q ) ( p q ) p q then write the compound proposition logically equivalent to p q using only the logical operator . Question 3: [40 points] a) [15 points] Let M ( x,y ) x has sent y and email message, where the domain consists of all students in your class. Use quantiers and logical connectives to express the following statement: There are two dierent students in your class who have sent each other email messages. b) [25 points] Use rules of inference to show that if x ( P ( x ) Q ( x )) and x ( ( P ( x ) Q ( x )) R ( x ) ) are true, then x ( R ( x ) P ( x )) is also true, where the domain of all quantiers are the same. [Indicate which rule was used at each step in your solution.] Scribble paper:...
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This note was uploaded on 01/27/2011 for the course ICS 253 taught by Professor Arnasser during the Spring '10 term at GWU.
 Spring '10
 ARNasser

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