Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If a and B Are Two Set Having 3 Elements in Common. If N(A) = 5, N(B) = 4, Find N(A × B) and N[(A × B) ∩ (B × A)]. - Mathematics

If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and n[(A × B) ∩ (B × A)].

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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, b, c) and (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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RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.1 | Q 8 | Page 8
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