Which statement given below is tautology ?

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Question

$	ext { (i) } p ightarrow( p \Lambda( p ightarrow q ))$

$(\sim p ) V ( p \Lambda(\sim p V q ))$

$(\sim p ) V ( f V ( p \Lambda q ))$

$\s

Vedclass · Accepted Answer

$( p \Lambda q ) \rightarrow(\sim( p ) \rightarrow q ))$

Vedclass · Answer

$	ext { (i) } p ightarrow( p \Lambda( p ightarrow q ))$

$(\sim p ) V ( p \Lambda(\sim p V q ))$

$(\sim p ) V ( f V ( p \Lambda q ))$

$\sim p V ( p \Lambda q )=(\sim p V p ) \Lambda(\sim p V q)$

$=\sim p V q$

$(ii)$ $( p \Lambda q ) ightarrow(\sim p ightarrow q )$

$\sim( p \Lambda q ) V ( p V q )= t$

$\{a, b, d\} V\{a, b, c\}=V$

Tautology

$(iii)$ $( p \Lambda( p ightarrow q )) ightarrow \sim q$

$\sim( p \Lambda(\sim p V q )) V \sim q =\sim( p \Lambda q ) V \sim q =\sim p V \sim q$

Not tantology

$(iv)$ $p V( p \Lambda q )= p$

Not tautology.

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