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Question 76567: Given: (~ p → q) ∨ ~ p
This statement is a:
A. Biconditional statement B. Self-Contradiction
C. Tautology D. Conjunction
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If we let p be false, then the entire disjunction is true since we would have
(~(false) → q) ∨ ~ (false)
(true → q) ∨ true
We can see that a disjunction is true if either side is true. Since the left side is true, the entire disjunction is true.
If we let p be true, then the entire disjunction is also true since we would have
(~(true) → q) ∨ ~ (true)
(false → q) ∨ false
Since a false antecedent means the entire implication is true, the whole left disjunct is true. This means the whole disjunction is true. So for any p (in this case q can be anything), the logical statement is true. This means the statement is a tautology (answer c).
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