Question

$A=\{x/xϵN,x^2-2x+1=0\}$ is sub set of:

• A. $A=\{x/xϵN,x^2=1\}$
• B. $A=\{x/xϵZ,x^2-2x+1=0\}$
• C. $A=\{x/xϵN,x=0\}$
• D. $A=\{x/xϵZ-Z^{+}\}$

Answer 1

Answer: (A), (B)

$A=\{x/xϵZ,x^2-2x+1=0\}$
$A=\{x/xϵN,x^2=1\}$

GIven $A=\{x|x\in N.x^2-2x+1=0\}$

$x^2-2x+1=0⟹(x-1{)}^2=0$

$x=1$

Considering option A, $x^2=1⟹x=\pm 1$

But given that $x\in N$. Hence $x=1$.

So this set contains the element $1$.

Hence given set $A$ is a subset of set given in option A.

Considering option B, $x^2-2x+1=0⟹x=1$.

Hence given set is a subset of set given in option B

Considering option C, $x=0$. Hence given set is not a subset of set given in option C.

Considering option D, $x$ is a negative integer. Hence $x=1$ is not present in that set. Hence given set is not a subset of set in option D.