Element Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Let

A = \{3, 7, 11, 15\}

. Determine whether

7 \in A

\{7\} \in A

, and

10 \notin A

1
Check $7 \in A$ : the element $7$ appears in the listing $\{3, 7, 11, 15\}$ , so $7 \in A$ . True.
2
Check $\{7\} \in A$ : the object $\{7\}$ is a set, not a number. The set $A$ does not contain $\{7\}$ as a member, only the number $7$ . So $\{7\} \notin A$ .
3
Check $10 \notin A$ : $10$ does not appear in the listing, so indeed $10 \notin A$ . True.

Answer

7 \in A,\quad \{7\} \notin A,\quad 10 \notin A

The symbol

\in

tests whether an object is a direct member of a set. A set

\{7\}

and the number

7

are different objects — confusing them is the most common mistake with element notation.

About Element

An individual object that belongs to, or is a member of, a given set — either it is in the set or it is not.

Let [formula]. Which of the following are true? (a) [formula], (b) [formula], (c) [formula], (d) [fo

Let [formula]. Fill in each blank with [formula] or [formula]: (a) [formula], (b) [formula], (c) [fo

Let [formula]. List all elements of [formula] and state [formula].