Question

If n(A) = 5, n(B) = 7 and n(AUB) = 10. then find n(A intersection B)
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Answer 1

Hint:

Before we solve this problem, let us know a set formula first. If A and B be two sets, then n(A) and n(B) are the numbers of their elements respectively. Then we have the relation,

n(A U B) = n(A) + n(B) - n(A ∩ B)

Step-by-step explanation:

Given, n(A) = 5, n(B) = 7, n(A U B) = 10

We know,

n(A U B) = n(A) + n(B) - n(A ∩ B)

⇒ n(A ∩ B) = n(A) + n(B) - n(A U B)

⇒ n(A ∩ B) = 5 + 7 - 10

⇒ n(A ∩ B) = 12 - 10

⇒ n(A ∩ B) = 2

Final answer: n(A ∩ B) = 2

The value of n(A ∩ B) is 2.