Given

A = {factors of 18}; A = {1, 2, 3, 6, 9, 18}

B = {multiples of 3 up to 27}; B = {3, 6, 9, 12, 15, 18, 21, 24, 27}

$\rm (A \cap B)$ = {3, 6, 9, 18}

$\rm (A \cup B)$ = {1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27}

U = {integers from 1 to 30}; U = {1, 2, 3, 4, 5, …, 26, 27, 28, 29, 30}

Showing the above information in a Venn diagram.

Hence, the cardinality of the required sets are given below:

$\rm n_{o} (A) = 2$

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

$\rm \therefore n(A \cup B) = 2 + 4+ 5 = 11$