Statement-1: The statement \(A\to(B\to A)\) is equivalent to \(A\to(A\vee B)\).
Statement-2: The statement \(\sim[(A\wedge B)\to(\sim A\vee B)]\) is a Tautology.
Statement-2: The statement \(\sim[(A\wedge B)\to(\sim A\vee B)]\) is a Tautology.
Show Hint
- Statement-1 is false; Statement-2 is true.
- Statement-1 is true; Statement-2 is true; Statement-2 is not correct explanation for Statement-1.
- Statement-1 is true; Statement-2 is false.
- Statement-1 is true; Statement-2 is true; Statement-2 is the correct explanation for Statement-1.
The Correct Option is C
Solution and Explanation
Statement-2: \((A\wedge B)\to(\sim A\vee B)=\sim(A\wedge B)\vee\sim A\vee B=\sim A\vee\sim B\vee\sim A\vee B\), which contains \(\sim B\vee B\), so it is a tautology. Its negation is therefore a contradiction, not a tautology. Statement-2 is false.
Answer: (3) Statement-1 is true; Statement-2 is false.
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