Question

If $A=\{x:2<x<7,x\text{is a prime number}\}$ and $B=\left\{\text{Odd numbers between 1 and 7}\right\}$, then $A$ and $B$ are ____ sets.

• A. disjoint
• B. overlapping
• C. equal
• D. equivalent

Answer 1

Answer: (B), (C), (D)

The correct options are
B overlapping
C equal
D equivalent

Given that $A=\{x:2<x<7,x\text{is a prime number}\}$ and $B=\left\{\text{Odd numbers between 1 and 7}\right\}$.
If $x$ is such that $2<x<7$, where $x$ is a prime number, then the possible values of $x$ are 3 and 5.
i.e., $A=\{3,5\}$
Also, 3 and 5 are the only odd numbers between 1 and 7.
Thus, $B=\{3,5\}$
$\therefore$ $A$ and $B$ are equal sets.
Equal sets are equivalent sets too.
Since $A$ and $B$ have (2) elements in common, they are overlapping sets as well.