The contrapositive of the statement "If x in | vedclass

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Question

(C) Let $p: x \in A$,$q: x \in B$,and $r: x \in A \cup B$.The given statement is $p \vee q \Rightarrow r$.The contrapositive of an implication $P \Rig

Vedclass · Accepted Answer

If $x 
otin A \cup B$,then $x 
otin A$ and $x 
otin B$

Vedclass · Answer

(C) Let $p: x \in A$,$q: x \in B$,and $r: x \in A \cup B$.The given statement is $p \vee q \Rightarrow r$.The contrapositive of an implication $P \Rightarrow Q$ is $\sim Q \Rightarrow \sim P$.Here,the contrapositive is $\sim r \Rightarrow \sim (p \vee q)$.Using De Morgan's Law,$\sim (p \vee q) \equiv (\sim p) \wedge (\sim q)$.Thus,the contrapositive is: If $x 
otin A \cup B$,then $x 
otin A$ and $x 
otin B$.

The contrapositive of the statement "If $x \in A$ or $x \in B$,then $x \in A \cup B$" is:

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