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Question

Since $0 \in A$ and $0$ does not belong to any of the sets $B, C, D$ and $E,$ it follows that, $A 
eq B, A 
eq C, A 
eq D, A 
eq E.$

Since $B =

Vedclass · Accepted Answer

Vedclass · Answer

Since $0 \in A$ and $0$ does not belong to any of the sets $B, C, D$ and $E,$ it follows that, $A 
eq B, A 
eq C, A 
eq D, A 
eq E.$

Since $B =\phi$ but none of the other sets are empty. Therefore $B 
eq C , B 
eq D$ and $B 
eq E$. Also $C =\{5\}$ but $-5 \in D$, hence $C 
eq D$.

Since $E =\{5\}, C = E .$ Further, $D =\{-5,5\}$ and $E =\{5\},$ we find that, $D 
eq E$

Thus, the only pair of equal sets is $C$ and $E .$

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\,\} $

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