Find the pairs of equal sets, if any, give reasons:
$A = \{ 0\} ,$
$B = \{ x:x\, > \,15$ and $x\, < \,5\} $
$C = \{ x:x - 5 = 0\} ,$
$D = \left\{ {x:{x^2} = 25} \right\}$
$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $
Find the pairs of equal sets, if any, give reasons:
$A = \{ 0\} ,$
$B = \{ x:x\, > \,15$ and $x\, < \,5\} $
$C = \{ x:x - 5 = 0\} ,$
$D = \left\{ {x:{x^2} = 25} \right\}$
$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $
Since $0 \in A$ and $0$ does not belong to any of the sets $B, C, D$ and $E,$ it follows that, $A \neq B, A \neq C, A \neq D, A \neq E.$
Since $B =\phi$ but none of the other sets are empty. Therefore $B \neq C , B \neq D$ and $B \neq E$. Also $C =\{5\}$ but $-5 \in D$, hence $C \neq D$.
Since $E =\{5\}, C = E .$ Further, $D =\{-5,5\}$ and $E =\{5\},$ we find that, $D \neq E$
Thus, the only pair of equal sets is $C$ and $E .$
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