Short Answer TypeR = {(a, b) : a ≤ b3}
(i) Since (a, a) ∉ R as a ≤ a3 is not always true
[Take a = 1/3. then a ≤ a3 is not true]
∴ R is not reflexive.
(ii) Also (a, b) ∈ R ⇏ (b, a) ∈ R
[Take a = 1, b = 4, ∴ 1 ≤ 43 but 4 ≰ (l)3 ]
∴ R is not symmetric.
(iii) Now (a, b) ∈ R, (b, c) ∈ R ⇏ (a, c) ∴ R
[Take a = 100, b = 5, c = 3, ∴ 100 ≤ 53, 5 ≤ 33 but 100 ≥ 33] R is not symmetric.
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
Switch
