Question

If n(U) = 360, n(A) = 240, n(B) = 160, find the maximum value of

n(AUB) and the minimum value of n(A n B). When will the value of
n(An B) be maximum and find its value.​

Answer 1

here is answer

Explanation:

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

= 240 + 160 - n(A n B)

= 400 - n(AnB )

Since n(AnB) 20, so n(AUB) S 400

But n(U) = 360, so n(A U B)* 360

.. the maximum value of n(AUB) = 360.

When n(A U B) is maximum, n(AnB) will be minimum.

.. min. value of n(An B)

= n(A) + n(B) - Max, value of n(AUB)

= 240 - 160 - 360 = 40

Again, n(

A B) will be maximum when B C A.

..the max. value of n(

A B) = n(B) = 160