Given:
A = {1, 2, 3}, B = {4} and C = {5}
A × (B ∪ C) = (A × B) ∪ (A × C)
Let us consider LHS: (B ∪ C)
(B ∪ C) = {4, 5}
A × (B ∪ C) = {1, 2, 3} × {4, 5}
= {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}
Now, RHS
(A × B) = {1, 2, 3} × {4}
= {(1, 4), (2, 4), (3, 4)}
(A × C) = {1, 2, 3} × {5}
= {(1, 5), (2, 5), (3, 5)}
(A × B) ∪ (A × C) = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)}
LHS = RHS
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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(i) Write R in roster form.
(ii) Find: dom (R) and range (R)
(iii) Write R–1 in roster form
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(i) Write R in roster form.
(ii) Find dom (R) and range (R).
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