Given:
A = {1, 2, 3} and B = {2, 4}
Now let us find: A × B, B × A, A × A, (A × B) ∩ (B × A)
A × B = {1, 2, 3} × {2, 4}
= {(1, 2), (1, 4), (2, 2), (2, 4), (3, 2), (3, 4)}
B × A = {2, 4} × {1, 2, 3}
= {(2, 1), (2, 2), (2, 3), (4, 1), (4, 2), (4, 3)}
A × A = {1, 2, 3} × {1, 2, 3}
= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
B × B = {2, 4} × {2, 4}
= {(2, 2), (2, 4), (4, 2), (4, 4)}
Intersection of two sets represents common elements of both the sets
So,
(A × B) ∩ (B × A) = {(2, 2)}
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.
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