Given,
A = {3, 5} and B = {7, 11}
R = {(a, b): a ∈ A, b ∈ B, a-b is odd}
On putting a = 3 and b = 7,
a – b = 3 – 7 = -4 which is not odd
On putting a = 3 and b = 11,
a – b = 3 – 11 = -8 which is not odd
On putting a = 5 and b = 7:
a – b = 5 – 7 = -2 which is not odd
On putting a = 5 and b = 11:
a – b = 5 – 11 = -6 which is not odd
∴ R = { } = Φ
R is an empty relation from A into B.
Hence proved.
Answered by Sakshi | 1 year agoLet R = {(a, b) : a, b, ϵ N and a < b}.Show that R is a binary relation on N, which is neither reflexive nor symmetric. Show that R is transitive.
Let A = {3, 4, 5, 6} and R = {(a, b) : a, b ϵ A and a
(i) Write R in roster form.
(ii) Find: dom (R) and range (R)
(iii) Write R–1 in roster form
Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.
Let R = {(x, x2) : x is a prime number less than 10}.
(i) Write R in roster form.
(ii) Find dom (R) and range (R).
If A = {5} and B = {5, 6}, write down all possible subsets of A × B.