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if n(U)=200 n(A)=160 n(B)=80 then least value of AUB is​

Sagot :

Olumideolawoyinidn

Answer:

160

Step-by-step explanation:

From the formula,

n (AUB) = n(A) + n(B) - n(A n B).

(AUB) has the least value when (A n B) has maximum possible value.

Therefore,

n (AUB) = n(A) + n(B) - maximum value of n(A n B).

We find maximum value of n(A n B) first.

Since (A n B) is a subset of B, so n(A n B) cannot be greater than n(B) = 80.

Therefore, maximum value of n(A n B) = 80.

Hence,

n (AUB) = n(A) + n(B) - maximum value of n(A n B)

n (AUB) = 160 + 80 - 80

n (AUB) = 160 + 0

n (AUB) = 160

The least value of AUB is 160.

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