Which of the following Boolean expressions is | vedclass

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Question

$(1)(\sim p \rightarrow q) \vee(\sim q \rightarrow p)$

$=(p \vee q) \vee(q \vee p)$

$=(p \vee p) \vee(q \vee q)$

$= \mathrm{p} \vee \mathrm{q

Vedclass · Accepted Answer

$(\sim \mathrm{p} \Rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \Rightarrow p)$

Vedclass · Answer

$(1)(\sim p \rightarrow q) \vee(\sim q \rightarrow p)$

$=(p \vee q) \vee(q \vee p)$

$=(p \vee p) \vee(q \vee q)$

$= \mathrm{p} \vee \mathrm{q}$

Which is not a tautology.

$(2)(q \rightarrow p) \vee(\sim q \rightarrow p)$

$=(\sim q \vee p) \vee(q \vee p)$

$=(\sim q \vee q) \vee p$

$= t \vee p=t$

$(3)(p \rightarrow q) \vee(\sim q \rightarrow p)$

$=(\sim p \vee q) \vee(q \vee p)$

$=(\sim p \vee p) \vee q$

$= t \vee q=t$

$(4)(p \rightarrow \sim q) \vee(\sim q \rightarrow p)$

$=(\sim p \vee \sim q) \vee(q \vee p)$

$=(\sim p \vee q) \vee(\sim q \vee q)$

$= t \vee t=t$

Which of the following Boolean expressions is not a tautology ?

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