Question

State, whether the following pairs of sets equal or not:

A={$x:x\in N$ and $x<3$} and B ={$y:y^2-3y+2=0$}

Answer 1

Step : Check whether the given pair of sets are equal

Given: A={$x:x\in N$ and $x<3$}
As, $x<3,x\in N$

$\Rightarrow x=\text{{1,2}}$

$\Rightarrow A=\text{{1,2}}$

B ={$y:y^2-3y+2=0$} [Given]

$\Rightarrow y^2-3y+2=0$

$\Rightarrow y^2-y-2y+2=0[-3y=-y-2y]$

$\Rightarrow y(y-1)-2(y-1)=0$

$\Rightarrow (y-1)(y-2)=0$

$\Rightarrow y=1ory=2$

$\Rightarrow$ B ={1, 2}

Therefore, elements of A and B are identical.

Hence, set A and B are equal.