Mathematical Reasoning
medium

આપેલ પૈકી ક્યૂ વિધાન સંપૂર્ણ સત્ય નથી ?

A

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

B

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

C

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

D

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

(JEE MAIN-2021)

Solution

$(1)(\sim p \rightarrow q) \vee(\sim q \rightarrow p)$

$=(p \vee q) \vee(q \vee p)$

$=(p \vee p) \vee(q \vee q)$

$= \mathrm{p} \vee \mathrm{q}$

Which is not a tautology.

$(2)(q \rightarrow p) \vee(\sim q \rightarrow p)$

$=(\sim q \vee p) \vee(q \vee p)$

$=(\sim q \vee q) \vee p$

$= t \vee p=t$

$(3)(p \rightarrow q) \vee(\sim q \rightarrow p)$

$=(\sim p \vee q) \vee(q \vee p)$

$=(\sim p \vee p) \vee q$

$= t \vee q=t$

$(4)(p \rightarrow \sim q) \vee(\sim q \rightarrow p)$

$=(\sim p \vee \sim q) \vee(q \vee p)$

$=(\sim p \vee q) \vee(\sim q \vee q)$

$= t \vee t=t$

Standard 11
Mathematics

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