Union Math Example 1

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

easy

Let

A = \{1, 3, 5\}

and

B = \{2, 3, 4\}

. Find

A \cup B

1
Recall the definition: $A \cup B = \{x : x \in A \text{ or } x \in B\}$ . The word 'or' is inclusive — an element belongs to the union if it appears in at least one of the sets.
2
List all elements from $A = \{1,3,5\}$ and $B = \{2,3,4\}$ , including each at most once: 1 (from $A$ ), 2 (from $B$ ), 3 (in both), 4 (from $B$ ), 5 (from $A$ ).
3
Therefore $A \cup B = \{1,2,3,4,5\}$ . Notice $|A \cup B| = 5 = |A| + |B| - |A \cap B| = 3 + 3 - 1$ , confirming the inclusion-exclusion principle.