Class 11

Math

JEE Main Questions

Sets

If X and 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?

$n(X∪Y)=60$

$n(X∩Y)=10$

We know,

$n(X∪Y)=n(X)+n(Y)−n(X∩Y)$

$⇒60=40+n(Y)−10$

$⇒n(Y)=30$

So, Set Y has $30$ elements.