This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MACM 101 Discrete Mathematics I Exercises on Propositional Logic. Due: Tuesday, Septem ber 29th (at the beginning of the class) SOLUTIONS 1. Construct a truth table for the following compound proposition: ( p q ) ( p q ) Solution p q ( p q ) ( p q ) 1 1 1 1 1 1 1 2. Which of the following statements are tautologies? ( p q ) ( p q ) ( p q ) ( ( p q )) ( p q ) ( p q ) Solution Method 1: Use truth tables. Method 2: Reason about it: 1) Yes, each of ( p q ) and ( p q ) is false if and only if p is true and q is false. 2) Yes, it follows from 1), De Morgans law and double negation law: ( p q ) ( p q ) ( p q ) ( ( p q )) ( p q ) ( ( p q )) ( p q ) ( ( p q )) 3) No, if we set p = 0 ,q = 1 then the formula turns into 0. 3. Show that ( p r ) ( q r ) and ( p q ) r are logically equivalent. Method 1: Use truth table. 1 Method 2: Use the laws of logic. ( p r ) ( q r ) (definition of ) ( p r ) ( q r ) (distributivity) ( p q ) r (De Morgan) ( ( p q )) r (definition of ) ( p q ) r 4. Show that ( a b c d e ) f and (...
View
Full
Document
 Spring '09
 jcliu
 Math, Logic

Click to edit the document details