Question

The sets

$A=\{x:x\in N\text{and}13>2x+1\}$ and

$B=\{y:y\in Z\text{and}-30\le y<-25\}$ are ___ sets.

• A. equal
• B. equivalent
• C. joint
• D. null

Answer 1

The correct option is B equivalent

$\text{Given}A=\{x:x\in N\text{and}13>2x+1\}.$

For $x\in N,$ $13>2x+1$
$\Rightarrow 12>2x$
$\Rightarrow 6>x$
i.e., $x<6$

$\therefore A=\{1,2,3,4,5\}$
$\Rightarrow n\left(A\right)=5$

$B=\{y:y\in Z\text{and}-30\le y<-25\}$
$\Rightarrow B=\{-30,-29,-28,-27,-26\}$
$\Rightarrow n\left(B\right)=5$

As $n\left(A\right)=n\left(B\right),$ the sets A and B are equivalent, though they are not equal.