Question 12556
A → (A ∨ q) is a ___________
- A.
Contingency
- B.
Tautology
- C.
Contradiction
- D.
None of the above
Attempted by 228 students.
Show answer & explanation
Correct answer: B
To determine the nature of the expression A → (A ∨ q), we use logical equivalences.
Step 1: Rewrite the implication using the equivalence A → B ≡ ¬A ∨ B.
A → (A ∨ q) ≡ ¬A ∨ (A ∨ q)
Step 2: Apply associativity of disjunction.
(¬A ∨ A) ∨ q
Step 3: ¬A ∨ A is a tautology, always true (T).
T ∨ q ≡ T
Since the expression simplifies to T, it is always true, meaning it is a tautology.