Negation of the statement (p vee r) Rightarro | vedclass

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(A) The negation of an implication $A \Rightarrow B$ is given by $A \wedge \sim B$.Therefore,$\sim((p \vee r) \Rightarrow (q \vee r)) = (p \vee r) \we

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$(p \wedge \sim q) \wedge \sim r$

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(A) The negation of an implication $A \Rightarrow B$ is given by $A \wedge \sim B$.Therefore,$\sim((p \vee r) \Rightarrow (q \vee r)) = (p \vee r) \wedge \sim(q \vee r)$.Using De Morgan's Law,$\sim(q \vee r) = (\sim q \wedge \sim r)$.So,the expression becomes $(p \vee r) \wedge (\sim q \wedge \sim r)$.By the distributive law,this is $((p \vee r) \wedge \sim r) \wedge \sim q$.Since $(p \vee r) \wedge \sim r = (p \wedge \sim r) \vee (r \wedge \sim r) = (p \wedge \sim r) \vee F = p \wedge \sim r$.Thus,the final expression is $(p \wedge \sim r) \wedge \sim q$,which is $p \wedge \sim q \wedge \sim r$.

Negation of the statement $(p \vee r) \Rightarrow (q \vee r)$ is :

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