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, $A^{\prime }=U-A$