Question

Given that n(e) = 23, n(A n B) = x, n(A) = y, n(B) = 2y and n(A' n B') = 7, find
the least possible value of y.​

Answer 1

Answer:

SO MINIMUM VALUE OF y=6

Step-by-step explanation:

n(U) = 23, n(A n B) = x, n(A) = y, n(B) = 2y and n(A' n B') = 7

n(A)=y so n(A')=23-y

n(B)=2y so n(B')=23-2y

(A' n B')= (AUB)'

so n(A' n B')=n (AUB)'=7

Thus n(AUB)=23-7=16

We know that

n(AUB)=n(A) +n(B) -n(A∩B)

So 16=y+2y-x

-x+3y=16......................(1)

3y=x+16

y=(x+16)/3

now as x so for y to be whole number

min x=2

and min y=(2+16)/3=18/3=6

SO MINIMUM VALUE OF y=6