If A and B are two sets such than n(A) = 8, n(B) = 11 and n(A ∪ B) = 14 then find n(A ∩ B).

Home » If A and B are two sets such than n(A) = 8, n(B) = 11 and n(A ∪ B) = 14 then find n(A ∩ B).

Given: n(A) = 8, n(B) = 11, n(A ∪ B) = 14
We know that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒ 14 = 8 + 11 – n(A ∩ B)
⇒ 14 = 19 – n(A ∩ B)
⇒ n(A ∩ B) = 19 – 14
⇒ n(A ∩ B) = 5
Hence n(A ∩ B) = 5

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More Material

In any ΔABC, prove that

If A = {x : x ε R, x < 5} and B = {x : x ε R, x > 4}, find A ∩ B.

Prove that A – B = A ∩ B.’

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Prove that A ∩ (A B)’ = φ

If A = {3, {2}}, find P(A).

If A = {5, 6, 7}, find P(A).

Let A = {x : x = 6n N) and B = {x : x = 9n, n ε N}, find A ∩ B.

If A ⊂ B, show that (B’ – A’) = φ.

If A ⊂ B, prove that B’ ⊂ A’.

If A and B are two sets such than n(A) = 54, n(B) = 39 and n(B – A) = 13 then find n(A ∪ B). Hint n(B) = n(B – A) + n(A ∩ B) ⇒ n(A ∩ B) = (39 – 13) = 26.

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