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JEE Math Practice Question

If the truth value of the statement $$(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$$ is F, then the truth value of which of the following is $$\mathrm{F}$$ ?

  1. A.$$\mathrm{P} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{R}$$
  2. B.$$\mathrm{R} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{P}$$
  3. C.$$\sim(\mathrm{P} \vee \mathrm{Q}) \rightarrow \sim \mathrm{R}$$
  4. D.$$\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \,\sim \mathrm{P}$$

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