The conditional statement
\( ((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q)) \) is :
The conditional statement
\( ((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q)) \) is :
Show Hint
- a tautology
- a contadiction
- equivalent to \( p \wedge q \)
- equivalent to \( ( \sim p) \vee r \)
The Correct Option is A
Solution and Explanation
Step 2: \( A\to B\equiv \sim A\vee B \) and \( B\to A\equiv \sim B\vee A \).
Step 3: Hence the statement \( \equiv \sim A\vee B\vee\sim B\vee A \).
Step 4: It contains both \( B\vee\sim B \) (and \( A\vee\sim A \)), which is always true. So it is a tautology.
Answer: (A) a tautology
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