Practice Intersection in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The intersection of sets A and B is the set of all elements that belong to both A and B simultaneously, written A \cap B.
Picture two overlapping circles in a Venn diagram—the intersection is only the overlapping region where both circles cover. For example, if set A is students who play soccer and set B is students who play piano, then A \cap B is students who do both. It is the AND gate of set theory: an element must satisfy both conditions to be included.
Example 1
easyLet A = \{1, 2, 3, 4\} and B = \{3, 4, 5, 6\}. Find A \cap B.
Example 2
mediumLet A = \{x \in \mathbb{R} : x \ge 1\} and B = \{x \in \mathbb{R} : x \le 4\}. Find A \cap B.
Example 3
easyLet M = \{2, 4, 6, 8\} and N = \{1, 2, 3, 4\}. Find M \cap N.
Example 4
easyFind A \cap B if A = \{2, 4, 6, 8\} and B = \{1, 2, 3, 4, 5\}.