Question

If the following pairs of sets are equivalent, enter $1$ or else enter $0$.

$A=\{x:xϵN\text{and}11\ge 2x-1\}$ and $B=\{y:yϵW\text{and}3\le y\le 9\}$.

Answer 1

Given : $A=\{x:xϵN\text{and}11\ge 2x-1\}$ and $B=\{y:yϵW\text{and}3\le y\le 9\}$.

For $A$,

$11\ge 2x-1$

$\Rightarrow 12\ge 2x$

$\Rightarrow 6\ge x$
Natural numbers less than and equal to $6$ are $1,2,3,4,5,6$
Hence, $A=\{1,2,3,4,5,6\}$
For set $B$,

$3\le y\le 9$

Whole numbers between $3$ and $9$ , including them are $3,4,5,6,7,8,9$
Hence, $B=\{3,4,5,6,7,8,9\}$

Number of elements in $A$ is $6$ and in $B$ is $7$.

Hence, they are not equivalent sets.

Hence, the answer is $0$.