NDA 2 2024 Maths, question 34

Topic: Algebra

Q34

Let $P$ and $Q$ be two non-void relations on a set $A$ . Which of the following statements are correct?

I. $P$ and $Q$ are reflexive $⇒P\cap Q$ is reflexive.

II. $P$ and $Q$ are symmetric $⇒P\cup Q$ is symmetric.

III. $P$ and $Q$ are transitive $⇒P\cap Q$ is transitive.

Select the answer using the code given below.

Solution.

Answer: (d) I, II and III

Every diagonal pair (a,a) belongs to both reflexive relations, so their intersection is reflexive.
If a pair is in the union of symmetric relations, its reverse is in the same relation and thus in the union.
If two composable pairs belong to the intersection of transitive relations, their implied pair belongs to both.
All three statements follow.