Question

Statement I Let $U$ be the universal set and $A$ be the subset of $U$. Then, complement of $A$ is the set of element of $A$.
Statement II The complement of a set $A$ can be represented by $A^{\prime}$.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (B)

Let $U$ be the universal set and $A$ is a subset of $U$. Then, the complement of $A$ is the set of all elements of $U$ which are not the elements of $A$. Symbolically, we write $A^{\prime}$ to denote the complement of $A$ with respect to $U$. Thus,
$ A^{\prime}=\{x: x \in U \text { and } x \notin A\}$
Obviously, $ A^{\prime}=U-A$