in Mathematical Logic retagged by
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in Mathematical Logic retagged by
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As you have given answer (B) so I guess you know about 2, 3
Now for 1

If we wanna prove that 1 is tautology we will prove by contradiction, we will try to make it false
We know $a\rightarrow b$ is false when $a = 1$ and $b=0$, so let $q = 0$

Now if we take $p=0$ then

$(\lnot p \land(p \lor q)) \rightarrow q = (1 \land(0 \lor 0)) \rightarrow 0 = 0 \rightarrow 0  = 1$

Let $p = 1$

$(\lnot p \land(p \lor q)) \rightarrow q = (0 \land(1 \lor 0)) \rightarrow 0 = 0 \rightarrow 0  = 1$

So (1) can never be false, hence (1) is tautology
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but in case of p=1, q=1 it doesn’t work
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all the statements are  tautology
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@h4kr When $q$ is $1$ how can given expression be false

We know in $a \rightarrow b$ if $b = 1$ then it doesn’t matter what $a$ is, it is always true. 

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thanks
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