15:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 16:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 17:T4f9,Let $x:(p \Delta q) \Rightarrow(p \Delta \sim q) \vee(\sim p \Delta q)$

Case-I

When $\Delta$ is same as $v$

Then $(p \Delta \sim q) \vee(\sim p \Delta q)$ becomes

$(p \vee \sim q) \vee(\sim p \vee q)$ which is always true, so $x$ becomes a tautology.

Case-II

When $\Delta$ is same as $\wedge$

Then $(p \wedge q) \Rightarrow(p \wedge \sim q) \vee(\sim p \wedge q)$

If $p \wedge q$ is $T$, then $(p \wedge \sim q) \vee(\sim p \wedge q)$ is $F$

so $x$ cannot be a tautology.

Case-III

When $\Delta$ is same as $\Rightarrow$

Then $(p \Rightarrow \sim q) \vee(\sim p \Rightarrow q)$ is same at $(\sim p \vee \sim q) \vee$ $(p \vee q)$, which is always true, so $x$ becomes a tautology.

Case-IV

When $\Delta$ is same as $\Leftrightarrow$

Then $(p \Leftrightarrow q) \Rightarrow(p \Leftrightarrow \sim q) \vee(\sim p \Leftrightarrow q)$

$p \Leftrightarrow q$ is true when $p$ and $q$ have same truth values, then $p \Leftrightarrow \sim q$ and $\sim p \Leftrightarrow q$ both are false. Hence $x$ cannot be a tautology.

So finally $x$ can be $\vee$ or $\Rightarrow$.

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