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 $x^2-2x-15=0\}$
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 $A\ne B,A\ne C,A\ne D,A\ne E$
Since, $B=\varphi$, but none of the other sets are empty. Therefore $B\ne C,B\ne D$ and $B\ne E$. Also, $C=\{5\}$ but - $5\in D$ hence $C\ne D$
Since, $E=\{5\},C=E$. Further, $D=\{-5,5\}$ and $E=\{5\}$, we find that $D\ne E$. Thus, the only one pair of equal sets is $C$ and $E$.