## Precalculus (6th Edition)

$(M' \cup Q) \cap R = \left\{0, 1, 2, 3, 4\right\}=R$
RECALL: (1) The symbol $\cap$ means the intersection of two sets, which lists down in a set the elements that are common to the given sets. (2) The symbol $\cup$ means the union of two sets, which lists down in a set the combined elements of the given sets. (3) $M'$ represents the complement of a set, which is the set that contains the elements of the universal set U that are not elements of M. Use (3) above to obtain: $M' = \left\{1, 3, 5, 7, 9, 10, 11, 12, 13\right\}$ Use (2) above to obtain: $M' \cup Q = \left\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\right\}$ Use (1) above to obtain: $(M' \cup Q) \cap R = \left\{0, 1, 2, 3, 4\right\}=R$