Given

P = {Multiples of 2 up to 20}; P = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

Q = {Multiples of 3 up to 24}; Q = {3, 6, 9, 12, 15, 18, 21, 24}

$\rm (P \cap Q)$ = {6, 12, 18}

$\rm (P \cup Q)$ = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24}

U = {Integers from 1 to 25}; U = {1, 2, 3, 4, 5, …, 21, 22, 23, 24, 25}

Showing the above information in a Venn diagram.

Hence,

$\rm n_{o} (P) = 7$

$\rm n(A \cup B) = n_{o}(P) + n(P \cap Q) + n_{o}(Q)$

$\rm \therefore n(A \cup B) = 7 + 3 + 5 = 15$