Question

If $A=\{x:x<5,x\text{is a natural number}\}$ and $B=\{x:-1<x<5,x\text{is an integer}\}$, then $A$ and $B$ are ___ sets.

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

Answer 1

The correct option is A disjoint

Given that $A=\{x:x<5,x\text{is a natural number}\}$ and $B=\{x:-1<x<5,x\text{is an integer}\}$.
If $x<5$, where $x$ is a natural number, then the possible values of $x$ are 1,2 3 and 4.
$⟹A=\{1,2,3,4\}$.
If $-1<x<5$, where $x$ is an integer, then the possible values of $x$ are 0, 1, 2, 3 and 4.
$⟹B=\{0,1,2,3,4\}$
Sets $A$ and $B$ have the elements 1, 2, 3 and 4 in common. Thus, $A$ and $B$ are not disjoint. They are overlapping sets.
Two sets are said to be overlapping sets if they have at least one element in common.
Sets $A$ and $B$ are not equivalent as the cardinalities are different. They are not equal sets as well.