Question

Taking the set of natural numbers as the universal set, match the complement set of following sets in Column I with the sets in Column II and choose the correct option from the codes given below.

Column I		Column II
A	$\{x:x$ is an even natural number $\}$	1	$\{x:x$ is not divisible by 15$\}$
B	$\{x:x$ is a prime number $\}$	2	$\{x:x$ is not a perfect square $\}$
C	$\{x:x$ is a multiple of 3$\}$	3	$\{x:x$ is an odd natural number $\}$
D	$\{x:x$ is a natural number divisible by 3 and $5\}$	4	$\{x:x$ is not a prime number $\}$
E	$\{x:x$ is a perfect square $\}$	5	$\{x:x$ is not a multiple of 3$\}$
F	$\{x:x$ is a perfect Cube$\}$	6	$\{x:x$ is not a perfect Cube $\}$

• A. A -(6), B -(5), C - (4), D -(3), E -(2), F -(1)
• B. A -(3), B -(4), C - (5), D -(1), E -(2), F -(6)
• C. A -(1), B -(2), C - (3), D -(4), E -(5), F -(6)
• D. A -(2), B -(3), C - (4), D -(5), E -(6), F -(1)

Answer 1

Answer: (B)

$U=$ Set of natural numbers
Let $A=\{x:x$ is an even natural number $\}$
$A^{\prime }=U-A$
$=\{x:x$ is an odd natural number $\}$
$B=\{x:x$ is a prime number $\}$
$B^{\prime }=U-B$
$=\{x:x$ is not a prime number $\}$
$C=\{x:x$ is a multiple of 3$\}$
$C^{\prime }=U-C$
$=\{x:x$ is not a multiple of 3$\}$
$D=\{x:x$ is a natural number divisible by 3 and 5$\}$
$=\{x:x$ is a natural number divisible by 15$\}$
$D^{\prime }=U-D$
$=\{x:x$ is a natural number not divisible by 15$\}$
$E=\{x:x$ is a perfect square $\}$
$E^{\prime }=U-E$
$=\{x:x$ is not a perfect square $\}$
$F=\{x:x$ is a perfect cube $\}$
$F^{\prime }=U-F=\{x:x$ is not a perfect cube $\}$