Question

Let A and B be two sets such that n(A)=0.16, n(B) =0.14,n(AUB)=0.25 . Then n(A ∩ B) is equal to

Answer 1

Answer:

GIVEN :

Let A and B be two sets such that n(A) = 0.16, n(B) = 0.14, n(A\bigcup B)=0.25n(A⋃B)=0.25 .

TO FIND :

The value of n(A\bigcap B)n(A⋂B)

SOLUTION :

Given that let A and B be two sets such that n(A) = 0.16, n(B) = 0.14, n(A\bigcup B) = 0.25n(A⋃B)=0.25 .

The formula is given by :

n(A\bigcup B)=n(A)+n(B)-n(A\bigcap B)n(A⋃B)=n(A)+n(B)−n(A⋂B) .

Substitute the values in the formula we get,

0.25=0.16+0.14-n(A\bigcap B)0.25=0.16+0.14−n(A⋂B) .

n(A\bigcap B)=0.16+0.14-0.25n(A⋂B)=0.16+0.14−0.25

=0.30-0.25=0.30−0.25

=0.05=0.05

∴ n(A\bigcap B)=0.05n(A⋂B)=0.05

∴ the value of n(A\bigcap B)n(A⋂B) is 0.05