If the statement
\(((\mathrm{p} * (\sim \mathrm{q})) \wedge(\mathrm{p} \vee \mathrm{q})) \Leftrightarrow \mathrm{p}\)
is a tautology, then \(*\) is :
\(((\mathrm{p} * (\sim \mathrm{q})) \wedge(\mathrm{p} \vee \mathrm{q})) \Leftrightarrow \mathrm{p}\)
is a tautology, then \(*\) is :
Show Hint
- \(\wedge\)
- \(\vee\)
- \(\Rightarrow\)
- \(\Leftrightarrow\)
The Correct Option is B
Solution and Explanation
Check the others: \(*=\wedge\) gives \(p\wedge\sim q\wedge(p\vee q)=p\wedge\sim q\), which differs from \(p\) when \(p=T,q=T\). \(*=\Rightarrow\) gives \((\sim p\vee\sim q)\wedge(p\vee q)\), which is false for \(p=q=T\) while \(p\) is true. \(*=\Leftrightarrow\) gives \((p\Leftrightarrow\sim q)\wedge(p\vee q)\), again false for \(p=q=T\).
Answer: (2) \(\vee\)
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