Question

Consider the following sets.
$A =\{0\}$,
$B =\{ x : x >15$ 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 $\left.x^{2}-2 x-15=0\right\}$
Choose the pair of equal sets

• A. A and B
• B. C and D
• C. C and E
• D. B and C

Answer 1

Answer: (C)

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 one pair of equal sets is $C$ and $E$.