A and B are two sets …
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Gaurav Seth 3 years, 6 months ago
n(A × B) = 5(4) = 20
n[(A × B) ∩ (B × A)] = 9
Step by step explanation:
Solution :
Given:
n(A) = 5 and n(B) = 4
Thus, we have:
n(A × B) = 5(4) = 20
A and B are two sets having 3 elements in common.
Now,
Let:
A = (a, a, a, b, c) and B = (a, a, a, d)
Thus, we have:
(A × B) = {(a, a), (a, a), (a, a), (a, d), (a, a), (a, a), (a, a), (a, d), (a, a), (a, a), (a, a), (a, d), (b, a),
(b, a), (b, a), (b, d), (c, a), (c, a), (c, a), (c, d)}
(B × A) = {(a, a), (a, a), (a, a), (a, b), (a, c), (a, a), (a, a), (a, a), (a, b), (a, c), (a, a), (a, a), (a, a),
(a, b), (a, c), (d, a), (d, a), (d, a), (d, b), (d, c)}
[(A × B) ∩ (B × A)] = {(a, a), (a, a), (a, a), (a, a), (a, a), (a, a), (a, a), (a, a), (a, a)}
∴ n[(A × B) ∩ (B × A)] = 9
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