Question

Which of the following statement pattern is a contradiction?

• A. S₄ ≡ (∼p ˄ q) ˅ (∼q)
• B. S₂ ≡ (p →q) ˅ (p ˄ ∼q)
• C. S₁ ≡ (∼p ˅ ∼q) ˅ (p ˅ ∼q)
• D. S₃ ≡ (∼p ˄ q) ˄ (∼q)

Answer 1

The Correct Option is D

To determine if a statement pattern is a contradiction, we are looking for a pattern that evaluates to false (contradiction) regardless of the truth values of the variables involved. 
By examining the statement patterns, we can see that the contradictory pattern is: 
(D) S₃ ≡ (∼p ˄ q) ˄ (∼q) 
In this pattern, the conjunction (∧) of (∼q) and (∼q) is contradictory because it states that q is both true and false at the same time. This results in a contradiction, making statement pattern (D) contradictory. 
Therefore, the statement pattern (D) is the contradiction.