Consider the two statements:


Consider the two statements:

$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology.

$(S 2):(p \wedge \sim q) \wedge(\sim p \vee q)$ is a fallacy.

Then :

  1. only (S1) is true.

  2. both $(\mathrm{S} 1)$ and $(\mathrm{S} 2)$ are false.

  3. both (S1) and (S2) are true.

  4. only (S2) is true.

Correct Option: , 3


$S_{1}:(\sim p \vee q) \vee(q \vee p)=(q \vee \sim p) \vee(q \vee p)$

$S_{1}=q \vee(\sim p \vee p)=q \vee t=t=$ tautology

$S_{2}:(p \wedge \sim q) \wedge(\sim p \vee q)=(p \wedge \sim q) \wedge \sim(p \wedge \sim q)=C$

$=$ fallacy

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