Question

If $U=\{1,2,3,4,5,6,7,8,9,10\};$ $D=\{1,3,6,9,10\}$ then find $D\text{'}$also find $n(D\text{'})$.

Answer 1

here $U=\{1,2,3,4,5,6,7,8,9,10\};D=\{1,3,6,9,10\}$

elements that are not available in set D but in the universal set, are 2,4,5,7,8

thus $D\text{'}=\{2,4,5,7,8\}$

now $n\left(D\right)=5\Rightarrow n(D\text{'})=10-5=5$

Complement of a set: The complement of a set is the set of elements present in the universal set but not in the given set.

The complement of a set A is written as A' and is read as a complement of set A.

Example: if universal set is {1,2,3,4,5,6,7,8,9,10} and A={2,3,5,7},then A'= {1,4,6,8,9,10}.

n= number of elements