Question

If set $A$ = { x : x is an odd natural number} and
set $B$ = { y: y is an even natural number}, then _____________________

• A. $A\cup B$ is a finite set.
• B. $A\cup B$ is a null set.
• C. $A\cap B$ is a null set.
• D. $A\cap B$ is an infinite set.

Answer 1

The correct option is C $A\cap B$ is a null set.

Set $A$ = { x : x is an odd natural number}
$\Rightarrow$ $A$ = { 1, 3, 5, 7,....}

Set $B$ = { y : y is an even natural number}
$\Rightarrow$ $B$ = { 2, 4, 6, 8,....}

$A\cup B$ = { 1, 3, 5, 7,....} $\cup$ { 2, 4, 6, 8,.....} = { 1, 2, 3, 4, 5, 6, 7, 8,.....} $\to$ This is an infinite set.

$A\cap B$ ={ 1, 3, 5, 7,....} $\cap$ { 2, 4, 6, 8,.....} = { } $\to$ This is a null set.