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JEE Math Practice Question

If P and Q are two statements, then which of the following compound statement is a tautology?

  1. A.((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ (P $$ \wedge $$ Q)
  2. B.((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ Q
  3. C.((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ P
  4. D.((P $$ \Rightarrow $$ Q) $$ \wedge $$ $$ \sim $$ Q) $$ \Rightarrow $$ $$ \sim $$ P

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