Which of the following propositions is a tautology?
1997
Which of the following propositions is a tautology?
- A.
(p ∨ q) → p
- B.
p ∨ (q → p)
- C.
p ∨ (p → q)
- D.
p → (p → q)
Attempted by 23 students.
Show answer & explanation
Correct answer: C
A tautology is a logical expression that is always True, no matter what truth values you give to p and q.
Let's test the correct expression from Option C: p OR (p -> q):
An implication
p -> qis automatically True whenever its starting variable (p) is False.Therefore, if
pis False, the right side(p -> q)becomes True -> the whole statement is True.If
pis True, the left side of the OR condition is True -> the whole statement is True.
Since it results in True under every single condition, it is a tautology.