Supply a reason for each step to show that the statement p→(q∨p) is a tautology. (Negation, Commutative, Universal Bound, Associative, Disjunctice Law)

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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Supply a reason for each step to show that the statement p→(q∨p) is a tautology. (Negation, Commutative, Universal Bound, Associative, Disjunctice Law)

 

note: refer to the image 

p→ (q V p) = ~p V (q V p)
= ~p V (p V q)
= (~p V p) V q
=tV q
Step 1
Step 2
Step 3
Step 4
Step 5
= t
Therefore, p → (q v p) is a tautology.
Transcribed Image Text:p→ (q V p) = ~p V (q V p) = ~p V (p V q) = (~p V p) V q =tV q Step 1 Step 2 Step 3 Step 4 Step 5 = t Therefore, p → (q v p) is a tautology.
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