Question

If X an Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

Answer 1

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Answer 2

SoluTion :-

Given

$\sf {\mapsto n(X)=40}\\\\\\\sf {\mapsto n=(X\ \cup Y)=60}\\\\\\\sf {\mapsto n(X \cap Y)=10}$

Now,

$\sf {n(X \cup Y)=n(X ) + n(Y)-n (X \cap Y)}\\\\\\\sf {60=40+n(Y)-10}\\\\\\\sf {60=30+n(Y)}\\\\\\\sf {n(Y)=60-30}\\\\\\\sf {n(Y)=30}$

Set Y has 30 elements.