Intersection Math Example 1

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

easy

Let

A = \{1, 2, 3, 4\}

and

B = \{3, 4, 5, 6\}

. Find

A \cap B

1
Recall the definition: $A \cap B = \{x : x \in A \text{ and } x \in B\}$ . An element belongs to the intersection only if it appears in both sets simultaneously.
2
Check each element of $A = \{1,2,3,4\}$ : is $1 \in B$ ? No. Is $2 \in B$ ? No. Is $3 \in B = \{3,4,5,6\}$ ? Yes. Is $4 \in B$ ? Yes.
3
The elements common to both sets are 3 and 4, so $A \cap B = \{3,4\}$ .