Question

Write out the following sets by listing their elements between braces. $$ \\{X: X \subseteq\\{3,2, a\\} \text { and }|X|=2\\} $$

Short answer

\{ \{3,2\}, \{3,a\}, \{2,a\} \}

Step-by-step solution

Understanding the Problem

We are given a set \{3, 2, a\} and we need to find all the subsets that contain exactly 2 elements. So we need to find pairs of elements from the original set.

Listing All Possible Subsets

Let's list all the subsets containing exactly 2 elements by making pairs: \{3,2\}, \{3,a\}, \{2,a\}. These are all the subsets from \{3,2,a\} that contains exactly 2 elements.

Presenting the Final Answer

Putting all those subsets together, the answer for the set \{X: X \subseteq \{3,2, a\} and |X|=2\} is \{ \{3,2\}, \{3,a\}, \{2,a\} \}.