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1. Prove or disprove the following using either equivalence laws or truth assignments (not truth tables). (a) p→ → (gr) ⇒ (p^¬r) → ¬q (b) ((pq) V (p^¬q)) ⇒ ((p↔¬q) ^ (p V q)) (c) (a + b)^ (b→ c) ⇒ (ac) 7

1. Prove or disprove the following using either equivalence laws or truth assignments (not truth tables). (a) p→ → (gr) ⇒ (p^¬r) → ¬q (b) ((pq) V (p^¬q)) ⇒ ((p↔¬q) ^ (p V q)) (c) (a + b)^ (b→ c) ⇒ (ac) 7

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 40E: 40. Prove or disprove that .
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Make sure you show for the first question clearly LS = RS (They both should be the same for the proof to be the same!)

 

1. Prove or disprove the following using either equivalence laws or truth assignments (not truth tables). (a) p→ (q→r) ⇒ (p^¬r) → ¬q ((5 ^ d-) v (b² ↔d)) ⇒ ((b- v d) ^ (b↔d)) - (9) L (c) (a → b) ^ (b→ c) ↔ (a → c)
Transcribed Image Text:1. Prove or disprove the following using either equivalence laws or truth assignments (not truth tables). (a) p→ (q→r) ⇒ (p^¬r) → ¬q ((5 ^ d-) v (b² ↔d)) ⇒ ((b- v d) ^ (b↔d)) - (9) L (c) (a → b) ^ (b→ c) ↔ (a → c)
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