Which of the following is not logically equiv | vedclass

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(B) Let $P$ be the statement "$A$ number is real" and $Q$ be the statement "$A$ number is rational or irrational".The given proposition is $P \implies

Vedclass · Accepted Answer

If a number is not rational or not irrational,then it is not real.

Vedclass · Answer

(B) Let $P$ be the statement "$A$ number is real" and $Q$ be the statement "$A$ number is rational or irrational".The given proposition is $P \implies Q$.The contrapositive of $P \implies Q$ is $
eg Q \implies 
eg P$.Here,$
eg Q$ is "$A$ number is neither rational nor irrational" and $
eg P$ is "$A$ number is not real".Thus,the contrapositive is: "If a number is neither rational nor irrational,then it is not real".Option $D$ is the original statement $P \implies Q$.Option $C$ is the contrapositive $
eg Q \implies 
eg P$.Option $A$ is also equivalent to the contrapositive.Option $B$ states: "If a number is not rational or not irrational,then it is not real". This is logically incorrect because a number can be irrational (not rational) and still be real,or rational (not irrational) and still be real. Thus,$B$ is not logically equivalent.

Which of the following is not logically equivalent to the proposition: "$A$ real number is either rational or irrational"?

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