QuestionDetermine if $\subseteq$ , $\subset$ , both, or neither fits in the blank for $\{10,18,16\} \_\{10,18,16,13\}$ . Choose the correct answer: only $C$ , only $\subseteq$ , both $\subseteq \& \subset$ , or none.

Studdy Solution

STEP 1

Assumptions1. The symbol $\subseteq$ denotes a set is a subset of another set or equal to it. . The symbol $\subset$ denotes a set is a proper subset of another set, meaning it is strictly contained within the other set and they are not equal.
3. The set $\{10,18,16\}$ is the set we are comparing to $\{10,18,16,13\}$ .

STEP 2

We can see that every element in the set $\{10,18,16\}$ is also in the set $\{10,18,16,13\}$ . Therefore, $\{10,18,16\}$ is a subset of $\{10,18,16,13\}$ .
$\{10,18,16\} \subseteq \{10,18,16,13\}$

STEP 3

However, the set $\{10,18,16\}$ is not equal to the set $\{10,18,16,13\}$ , because the latter set has an additional element,13. Therefore, $\{10,18,16\}$ is a proper subset of $\{10,18,16,13\}$ .
$\{10,18,16\} \subset \{10,18,16,13\}$

STEP 4

Therefore, both $\subseteq$ and $\subset$ can be placed in the blank to make the statement true.The correct answer is "both $\subseteq \& \subset$ ".

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