Question 76567
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).