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

Answer: (D)

S3 ≡ (∼p ˄ q) ˄ (∼q)

Answer 2

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.