Idempotency law is I. I. P Ú P = P. II. P Ù P = P. III. P + P = P. A. Only (I) B. Only (II) C. Only (III) D. Both (I) and (II)

The correct answer is D. Both (I) and (II).

Idempotency law is a law of logic that states that the result of applying a logical operation to a value twice is the same as applying it once. In other words, if $P$ is a logical value, then $P \land P = P$ and $P \lor P = P$.

Option I is the statement $P \land P = P$. This is the law of idempotence for conjunction. Option II is the statement $P \lor P = P$. This is the law of idempotence for disjunction. Both of these statements are true, so the correct answer is D. Both (I) and (II).

Here is a more detailed explanation

• Option I: $P \land P = P$. This is the law of idempotence for conjunction. Conjunction is a logical operation that takes two values and returns a value that is true if both of the original values are true. The law of idempotence for conjunction states that if $P$ is a logical value, then $P \land P = P$. This means that if $P$ is true, then $P \land P$ is also true. This is because $P \land P$ is just $P$ repeated twice.
• Option II: $P \lor P = P$. This is the law of idempotence for disjunction. Disjunction is a
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  logical operation that takes two values and returns a value that is true if either of the original values are true. The law of idempotence for disjunction states that if $P$ is a logical value, then $P \lor P = P$. This means that if $P$ is true, then $P \lor P$ is also true. This is because $P \lor P$ is just $P$ repeated twice.

I hope this explanation is helpful!