Question

Which of the following statements is contingency?

Options

• (p v q) v ~ q

• (p v q) v ~ p

• (p v q) ∧ ~ q

• p → (p v q)

Answer 1

(p v q) ∧ ~ q

Explanation:

A statement which is neither a tautology nor a contradiction is a contingency.

1st option: (p v q) v ~ q

≡ p v (q v ~ q)

≡ p v T

≡ T which is a tautology.

2nd option: (p v q) v ~ p

≡ (p v ~ p) v q

≡ T v q

≡ T which is tautology.

3rd option: (p v q) ∧ ~ q

≡ (p ∧ ~ q) v (q ∧ ~ q)

≡ (p ∧ ~ q) v F

≡ (p ∧ ~ q)

if p → T, q → T

Then p ∧ ~ q → F

if p → T, q → T

Then p ∧ ~ q → T

So, (p ∧ ~ q) is a contingency.

Therefore statement (p v q) ∧ ~ q is contingency.