Question

Which of the following is a tautology?

• A. (P $\rightarrow$ Q) $\rightarrow$ (Q $\rightarrow$ P)
• B. (P $\cap$ Q) $\rightarrow$ (P $\cup$ Q)
• C. (P $\cup$ Q) $\rightarrow$ (Q $\cap$ P)
• D. (P $\cap$ Q) $\rightarrow$ (\neg P)

Hint:

To identify tautologies, check if the statement is always true regardless of the truth values of individual components.

Answer 1

The Correct Option is B

A tautology is a logical statement that is always true regardless of the truth values of its components. The correct statement that is always true is \( (P \cap Q) \rightarrow (P \cup Q) \). This is because the intersection of two sets \( P \cap Q \) is always a subset of their union \( P \cup Q \), and hence the implication is always true.
Thus, the correct answer is \( (P \cap Q) \rightarrow (P \cup Q) \).