Supply a reason for each step in the solution below showing ((p→ q) → plp is a tautology. [(p - q) - p] → p = [(p q) → p] V p = -[~(p q) V p] v p = -[~(~p v q) V p] v p = [(~p v q) A~p] V p = [mp^(~p v q)] vp Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 = ~p Vp Thererefore, [(p → q) p] p is a tautology.
Supply a reason for each step in the solution below showing ((p→ q) → plp is a tautology. [(p - q) - p] → p = [(p q) → p] V p = -[~(p q) V p] v p = -[~(~p v q) V p] v p = [(~p v q) A~p] V p = [mp^(~p v q)] vp Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 = ~p Vp Thererefore, [(p → q) p] p is a tautology.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Topic Video
Question
State if the following step are:
- Negation Law
- De Morgan's Law
- Disjunctive form
- Absorption law
- Cummutative Law
![Supply a reason for each step in the solution below showing [(p → q) → p] → p is a tautology.
Step 1
Step 2
[(p → q) - p] →p = ~[(p→q) → p] V p
= -[~(p → q) V p] v p
= -[~(~p V q) v p] V p
= [(~p v q) A~p] V p
= [mpA(~p v q)] v p
= "p Vp
Step 3
Step 4
Step 5
Step 6
Step 7
=t
Thererefore, [(p q) p] p is a tautology.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b0ce941-6bfd-4f1f-a165-d8888effee8c%2F59eb7a65-e3c2-4fde-a773-2b67b444c4bf%2F0c1hk0t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Supply a reason for each step in the solution below showing [(p → q) → p] → p is a tautology.
Step 1
Step 2
[(p → q) - p] →p = ~[(p→q) → p] V p
= -[~(p → q) V p] v p
= -[~(~p V q) v p] V p
= [(~p v q) A~p] V p
= [mpA(~p v q)] v p
= "p Vp
Step 3
Step 4
Step 5
Step 6
Step 7
=t
Thererefore, [(p q) p] p is a tautology.
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