Question

which of the following are subsets of $n = \\{5, 10, 15\\}$? select all that apply.
$\\{5, 10\\}$
$\\{20\\}$
$\\{5, 15\\}$
$\\{5, 10, 15\\}$

Explanation:

Step1: Define subset rule

A set $S$ is a subset of $N$ if every element of $S$ is in $N=\{5,10,15\}$.

Step2: Check $\{5,10\}$

All elements $5,10 \in N$, so it is a subset.

Step3: Check $\{20\}$

$20
otin N$, so it is not a subset.

Step4: Check $\{5,15\}$

All elements $5,15 \in N$, so it is a subset.

Step5: Check $\{5,10,15\}$

A set is a subset of itself, so it is a subset.

Answer:

• $\{5, 10\}$
• $\{5, 15\}$
• $\{5, 10, 15\}$