Midterm 1

# Midterm 1 - Problem Mark 1 2 3 4 5 6 7 Total MACM 101 Last...

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Problem 1 2 3 4 5 6 7 Total Mark MACM 101 Midterm Test October 6, 2010 Last Name First Name and Initials Student No. NO AIDS allowed. Answer ALL questions on the test paper. Use backs of sheets for scratch work. Total Marks: 100 1. Prove that ( r p ) ( r q ) and r ( p q ) are logically equivalent. Use logical equivalences. Justify every step. [12] Solution: ( r p ) ( r q )) ⇐⇒ ( ¬ r p ) ( ¬ r q ) expression for implications ⇐⇒ ¬ r ( p q ) distributive law ⇐⇒ r ( p q ) expression for implication 2. Prove that the Rule of Modus Tollens is a valid argument. [14] Solution: It suﬃces to prove that the corresponding expression (( p q ) ∧ ¬ q ) → ¬ p is a tautology. Method 1. Construct the truth table. The table should be given. Method 2. Use logical equivalences to show that this statement is equiva- lent to 1 (True). All steps must be justﬁﬁed.

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3. Prove without using Venn diagrams: A B A B . [15]
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## This note was uploaded on 12/12/2010 for the course MACM 101 taught by Professor Pearce during the Summer '08 term at Simon Fraser.

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Midterm 1 - Problem Mark 1 2 3 4 5 6 7 Total MACM 101 Last...

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