Write in symbols: the complement of the union of sets $A$ and $B$ .
A) $\bar { A } \cup \bar { B }$
B) $\overline { A \cup B }$
C) $\bar { A } \cup B$
D) $\overline { A \cap B }$
E) $\bar { A } \cap \bar { B }$

Question

Quizplus · Accepted Answer

The complement of the union of sets $A$ and $B$ is the set of all elements that are not in either $A$ or $B$ or both. This is represented by $\overline { A \cup B }$ which reads "the complement of the union of sets A and B". Option A is the complement of both sets individually, which is not what we want. Option C is the complement of $A$ and the union of $\bar { A }$ and $B$, which is different from what we want. Option D is the complement of the intersection of sets $A$ and $B$, which is not what we want either. Option E is the intersection of the complements of both sets, which is also different from what we want. Therefore, B is the best representation of the complement of the union of sets $A$ and $B$.

Write in Symbols: the Complement of the Union of Sets AAA

Write in Symbols: the Complement of the Union of Sets $A$