Venn Diagrams — Practice Quiz

A Set Theory cheat sheet for Venn Diagrams — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

AB
Union A ∪ B — shaded: everything in either set
$$A \cup B$$
AB
Intersection A ∩ B — shaded: only the overlap
$$A \cap B$$
AB
Difference A minus B — shaded: in A but not B
$$A \setminus B$$
AU
Complement Aᶜ — shaded: everything outside A within U
$$A^{c}$$
AB
Symmetric difference A △ B — shaded: in exactly one set
$$A \triangle B$$
AB
Subset A ⊆ B — A sits entirely inside B
$$A \subseteq B$$
AB
Disjoint A ∩ B = ∅ — no overlap
$$A \cap B = \varnothing$$

Practice quiz

  1. If $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$, what is $A \cup B$?

    • $\{1, 2, 3, 4, 5\}$
    • $\{3\}$
    • $\{1, 2\}$
    • $\{4, 5\}$

    Answer: $\{1, 2, 3, 4, 5\}$

  2. Given sets $X = \{a, b, c, d\}$ and $Y = \{c, d, e, f\}$, find $X \cap Y$.

    • $\{a, b, c, d, e, f\}$
    • $\{c, d\}$
    • $\{a, b\}$
    • $\{e, f\}$

    Answer: $\{c, d\}$

  3. Let $P = \{apple, banana, cherry\}$ and $Q = \{banana, grape\}$. What is $P \setminus Q$?

    • $\{apple, cherry\}$
    • $\{banana\}$
    • $\{apple, banana, cherry, grape\}$
    • $\{grape\}$

    Answer: $\{apple, cherry\}$

  4. If the universal set is $U = \{1, 2, 3, 4, 5\}$ and $A = \{2, 4\}$, what is $A^c$?

    • $\{2, 4\}$
    • $\{1, 3, 5\}$
    • $\{1, 2, 3, 4, 5\}$
    • $\varnothing$

    Answer: $\{1, 3, 5\}$

  5. For sets $M = \{x, y, z\}$ and $N = \{y, w\}$, what is $M \triangle N$?

    • $\{y\}$
    • $\{x, z, w\}$
    • $\{x, y, z, w\}$
    • $\varnothing$

    Answer: $\{x, z, w\}$

  6. Which of the following statements is true?

    • $\{1, 2, 3\} \subseteq \{1, 2\}$
    • $\{a, b\} \subseteq \{a, b, c\}$
    • $\{x, y, z\} \subseteq \{x, y\}$
    • $\varnothing \subseteq \{1\}$ is false.

    Answer: $\{a, b\} \subseteq \{a, b, c\}$

  7. Which pair of sets is disjoint?

    • $A = \{1, 2\}$, $B = \{2, 3\}$
    • $C = \{a, b\}$, $D = \{c, d\}$
    • $E = \{red, blue\}$, $F = \{blue, green\}$
    • $G = \{even \text{ numbers}\}$, $H = \{multiples \text{ of } 2\}$

    Answer: $C = \{a, b\}$, $D = \{c, d\}$

  8. Given $U = \{1, 2, 3, 4, 5, 6\}$, $A = \{1, 2, 3\}$, $B = \{3, 4, 5\}$. What is $(A \cup B)^c$?

    • $\{1, 2, 3, 4, 5\}$
    • $\{6\}$
    • $\{3\}$
    • $\{1, 2, 4, 5\}$

    Answer: $\{6\}$

  9. Let $S = \{p, q, r, s\}$ and $T = \{q, s, t\}$. Find $(S \setminus T) \cup (T \setminus S)$.

    • $\{q, s\}$
    • $\{p, r, t\}$
    • $\{p, q, r, s, t\}$
    • $\varnothing$

    Answer: $\{p, r, t\}$

  10. If $A \cap B = \varnothing$, which of the following must be true?

    • $A \subseteq B$
    • $B \subseteq A$
    • $A \triangle B = A \cup B$
    • $A \cup B = \varnothing$

    Answer: $A \triangle B = A \cup B$

Select a subject

Select a subject from the left panel to begin exploring formulas.