Question

$(p \land q) \lor (\sim p \land \sim q)$ is

• A. a contradiction
• B. a tautology
• C. either (a) or (b)
• D. neither (a) nor (b)

Hint:

$(p \land q) \lor (\sim p \land \sim q)$ is equivalent to $p \leftrightarrow q$.

Answer 1

The Correct Option is D

Step 1: Basic Principle
Construct truth table to check if the statement is tautology or contradiction.
Step 2: Solution Procedure:
$(p \land q) \lor (\sim p \land \sim q)$ means "both p and q are true OR both p and q are false". This is the biconditional $p \leftrightarrow q$.
Truth table:
When p and q are both true: T
When p and q are both false: T
When p true, q false: F
When p false, q true: F
So it is not always true (not tautology) and not always false (not contradiction). It is a contingency.
Step 3: Required Answer:
It is neither a tautology nor a contradiction.