Question

Which of the following sets are the subsets of $A=\{k:k\text{is a factor of}48\}?$

• A. $\{1,2,4,8\}$
• B. $\{1,12,16,24,48\}$
• C. $\{1,48\}$
• D. $\{1,2,3,4,6,8,12,24,48\}$

Answer 1

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

$\{1,2,3,4,6,8,12,24,48\}$

Given $A=\{k:k\text{is a factor of}48\}$
In roster form:
$A=\{1,2,3,4,6,8,12,16,24,48\}$

Any set $X$ is a subset of $A,$ if each and every element of $X$ is also an element of $A,$ or if $k\in X\Rightarrow k\in A.$

Now, looking at the options, we can conclude that each set is a subset to $A.$