Question

Which of the following is a superset of the set $X=\{k:k\text{is a factor of}6\}?$

• A. $M=\{m:m\text{is a factor of 12}\}$
• B. $N=\{n:n\text{is a factor of 24}\}$
• C. $O=\{o:o\text{is a factor of 36}\}$
• D. $P=\{p:p\text{is a factor of 48}\}$

Answer 1

Answer: (A), (B), (C), (D)

$P=\{p:p\text{is a factor of 48}\}$

Given $X=\{k:k\text{is a factor of 6}\}$
In Roster form we can write the set as $X=\{1,2,3,6\}$

Now, If any set $A$ is a subset of another set $B,$ then $B$ is called as the superset of $A.$

That means, for any of these sets to be a superset of $X,X$ needs be to be it's subset.

Here, since we know $6$ is a factor of $12,24,36\&48.$
This implies $X$ is a subset of all the sets $M,N,O,P.$

Thus all these sets are supersets of $X.$