Class 11

Math

Co-ordinate Geometry

Sets

If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S∩T$ has $11$ elements, how many elements does $S∪T$ have?

$n(S)=21,n(T)=32,n(S∩T)=11$

We know that:

$n(S∪T)=n(S)+n(T)−n(S∩T)$

$∴n(S∪T)=21+32−11=42$

Thus, the set $(S∪T)$ has 42 elements.