Homework1

# Homework1 - Homework#1 Q1 Prove the first distributive law...

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Homework #1 Q1. Prove the first distributive law on slide 8 of unit 1.3 slides, using a truth table. p ( q r ) ( p q ) ( p r ) p q r q∧r p∨q p∨r p∨(q∧ r) (p∨q) ∧ (p∨r) T T T T T T T T T T F F T T T T T F T F T T T T T F F F T T T T F T T T T T T T F T F F T F F F F F T F F T F F F F F F F F F F Q2. Exercise 32, p. 15, item d) (p ∧ q) → (p ∨ q) p Q p∧q p∨q (p∧q) → (p ∨ q) T T T T T T F F T T F T F T T F F F F T Q3. Exercise 36, p. 15, item f) (p∧q)∨¬r p q r ¬r p∧q (p∧q)∨¬r T T T F T T T T F T T T T F T F F F T F F T F T F T T F F F F T F T F T F F T F F F F F F T F T

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Q4. Exercise 18, p. 112 Suppose that the truth value of the proposition p i is T whenever i is an odd positive integer and is F whenever i is an even positive integer. Find the truth values of ¿ i = 1 ¿ 100 ( p i p i + 1 ) and p i + 1 p i ¿ ¿ ¿ ¿ i = 1 ¿ 100 ¿ ¿ i = 1 ¿ 100 ( p i p i + 1 ) is false because two consecutive numbers will not both be odd. p i + 1 p i ¿ ¿ ¿ ¿ i = 1 ¿ 100 ¿ is true because either p i is odd or p i+1 is odd for every i . When
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