Is B = x : x ^2+2 x +1=0, x N a singleton set? - Vidyadip

Question

Is $B =\left\{ x : x ^2+2 x +1=0, x \in N \right\}$ a singleton set?

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Answer

We have, $B=\left\{x: x^2+2 x+1=0, x \in N\right]$
Now, $x^2+2 x+1=0$
$\Rightarrow(x+1)^2=0$
$\Rightarrow x=-1$ which is not a natural number.
Thus. $B =\{ \}=\phi$
Hence, B is not a singleton set.

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