Let's find the complement of the union of sets P and Q, given the universal set U and the definitions of sets P and Q.

U = {Even numbers between 0 and 30} = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}

P = {Multiples of 6 between 0 and 30} = {0, 6, 12, 18, 24, 30}

Q = {Multiples of 4 between 0 and 30} = {0, 4, 8, 12, 16, 20, 24, 28}

The union of two sets is the set of all elements that are in either set. So,

P ∪ Q = {0,4,6,8,12,16,18,20,24,28,30}

The complement of a set A with respect to a universal set U is the set of all elements in U that are not in A. So,

(P ∪ Q)ᶜ = U - (P ∪ Q) = {2 ,10 ,14 ,22 ,26}

This is the set of all elements that are in U but not in P or Q.