Negation of the compound proposition: "If the | vedclass

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(B) Let $p$ be the statement: "The examination is difficult".Let $q$ be the statement: "$I$ shall pass".Let $r$ be the statement: "$I$ study hard".The

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

Vedclass · Answer

(B) Let $p$ be the statement: "The examination is difficult".Let $q$ be the statement: "$I$ shall pass".Let $r$ be the statement: "$I$ study hard".The given proposition is: $p \Rightarrow (r \Rightarrow q)$.We know that the negation of an implication $A \Rightarrow B$ is $A \wedge \sim B$.Therefore,$\sim(p \Rightarrow (r \Rightarrow q)) \equiv p \wedge \sim(r \Rightarrow q)$.Since $\sim(r \Rightarrow q) \equiv r \wedge \sim q$,the negation is $p \wedge (r \wedge \sim q)$.This translates to: "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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