Question

if A and B are two sets having 3 elements in common. if n(A)=5, n(B)=4, find n(A*B) and n[(A*B) intersection (B*A)].

Answer 1

Answer:

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

Answer 2

Answer:

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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