Question

If X and Y are two sets such that X union Y has 50 elements , X has 28 elements and Y has 32 elements, how many elements X intersection Y have?
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Answer 1

X U Y = 50

X ∩ Y =?

n(x U y)=n(x)+n(y)- n(X ∩ Y)

50=28+32-n(X ∩ Y)

50-28-32=-n(X ∩ Y)

-10=-n(X ∩ Y)

therefore X ∩ Y= 10

Answer 2

Answer:

n(XUY) = 50

n(X) = 28

n(Y) = 32

n(XnY) = n(X)+n(Y)-n(XUY)

or, n(XnY) = 60-50 = 10