Short Answer TypeSince R and R’ are relations on a set A.
∴ R ⊆ A x A and R’ ⊆ A x A.
⇒ R ∪ R’ ⊆ A x A and R ∩ R’ ⊆ A x A.
∴ R ∪ R’ and R ∩ R’ are also relations on the set A.
We now show that R ∪ R’ is reflesive relation on A.
Let a ∈ A.
∴ (a, a) ∈ R and (a. a) ∈ R’. (∵ R and R’ are reflexive on A)
⇒ (a. a) ∈ R ∪ R’ and R ∩ R’ ∀ a ∈ A.
∴ R ∪ R’ and R ∩ R’ are reflexive relations on A.
Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}.
Choose the correct answer.
(A) (2. 4) ∈ R (B) (3, 8) ∈ R (C) (6,8) ∈ R (D)(8,7) ∈ R
Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is
(A) 1 (B) 2 (C) 3 (D) 4
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