Given the following two statements:

Question:

Given the following two statements:

$\left(S_{1}\right):(q \vee p) \rightarrow(p \leftrightarrow \sim q)$ is a tautology.

$\left(S_{2}\right): \sim q \wedge(\sim p \leftrightarrow q)$ is a fallacy.

Then :

  1. only $\left(\mathrm{S}_{1}\right)$ is correct.

  2. both $\left(S_{1}\right)$ and $\left(S_{2}\right)$ are correct.

  3. both $\left(S_{1}\right)$ and $\left(S_{2}\right)$ are not correct.

  4. only $\left(S_{2}\right)$ is correct.

Correct Option: , 3

Solution:

Let TV(r) denotes truth value of a statement $\mathbf{r}$.

Now, if $\mathrm{TV}(\mathrm{p})=\mathrm{TV}(\mathrm{q})=\mathrm{T}$

$\Rightarrow \mathrm{TV}\left(\mathrm{S}_{1}\right)=\mathrm{F}$

Also, if $T V(p)=T \& T V(q)=F$

$\Rightarrow \mathrm{TV}\left(\mathrm{S}_{2}\right)=\mathrm{T}$

 

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