Question

Which of the following statement pattern is a tautology?

पर्याय

• (p → q) v q

• p → (q v q)

• (p v q) → q

• p v (q → p)

Answer 1

p → (q v q)

Explanation:

1st option, (p → q) v q

≡ (~ p v q) v q

≡ (~ p v q)

It is not a tautology since if p is true and q is false then (~ p v q) is false.

2nd option, p → (q v q)

≡ ~ p v (q v p)

≡ (~ p v p) v q

≡ T v q    ...(∵ ~ p v p ≡ T)

it is a tautology since if q is true or false then T v q must be true.