Negation of the compound proposition : If the | vedclass

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Question

(b) $p :$ examination is difficult,
$q :$ I shall pass,
$r :$ I study hard
Given result is :  $p \Rightarrow (r \Rightarrow q)$
Now $\s

Vedclass · Accepted Answer

The examination is difficult and I study hard but I shall not pass

Vedclass · Answer

(b) $p :$ examination is difficult,
$q :$ I shall pass,
$r :$ I study hard
Given result is :  $p \Rightarrow (r \Rightarrow q)$
Now $\sim(r \Rightarrow q)$ $= r \wedge \sim q$
$\sim(p \Rightarrow (r \Rightarrow q)) \equiv p \wedge (r\; \wedge \sim\,q)$
The examination is difficult and I study hard but I shall not pass.

Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard

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