#### Answer

$(R \cup N) \cap M' = \left\{3, 5, 7, 9, 11, 13\right\}$

#### Work Step by Step

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 (2) above to obtain:
$R \cup N = \left\{0, 1, 2, 3, 4, 5, 7, 9, 11, 13\right\}$
Use (3) above to obtain:
$M' = \left\{1, 3, 5, 7, 9, 10, 11, 12, 13\right\}$
Use (1) above to obtain:
$(R \cup N) \cap M' = \left\{3, 5, 7, 9, 11, 13\right\}$