4. -[lp A~ q) A r] = ¬p V q V ¬r 5. -[p → (¬q)] = p A q 6. (p → r) A (q → r) = (p V q) → r

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.3: The Field Of Quotients Of An Integral Domain
Problem 6E
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Note: Only solve the sub-part (numbers 4,5, and 6 only)

b. Prove that the following are logically equivalent.
1. (p V q)
(q → q) = r
2. (p A ¬q) v q = p V q
3. -(р А q) А q рАq
4. -[lp A~ q) A r] = "p V q v ¬r
5. -[p → (¬q)] = p A q
6. (p → r) A (q → r) = (p V q) → r
Transcribed Image Text:b. Prove that the following are logically equivalent. 1. (p V q) (q → q) = r 2. (p A ¬q) v q = p V q 3. -(р А q) А q рАq 4. -[lp A~ q) A r] = "p V q v ¬r 5. -[p → (¬q)] = p A q 6. (p → r) A (q → r) = (p V q) → r
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