Question

if n(A)=25,n(B)=40,n(AuB)=50 and n(B')=25,find n(AnB) and n(U) .

Answer 1

Hey there !

Here's the answer !

Given : n ( A ) = 25 ; n ( B ) = 40 ; n ( A U B ) = 50 ; n ( B¹ ) = 25

Formula to be used : n ( A U B ) = n ( A ) + n ( B ) - n ( A ∩ B )

Substituting the given values in the above formula we get,

=> 50 = 25 + 40 - n ( A ∩ B )

=> n ( A ∩ B ) = 25 + 40 - 50

=> n ( A ∩ B ) = 65 - 50 = 15

Hence n ( A ∩ B ) = 15

We also know that,

n ( B¹ ) = n ( U ) - n ( B )

Substituting the values we get,

25 = n ( U ) - 40

=> n ( U ) = 40 + 25 = 65.

Hence the universal set n ( U ) contains 65 elements.

Hope it helped !

Answer 2

Answer:

65

Step-by-step explanation: