If n(B) = 13, n(A ∪ B) = 20, and n(A ∩ B) = 5, find n(A).

To find the cardinality (number of elements) of set A, we can use the following formula:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Given that n(A ∪ B) = 20, n(B) = 13, and n(A ∩ B) = 5, we can substitute these values into the formula to find n(A):

20 = n(A) + 13 - 5

To isolate n(A), we can subtract 13 from both sides of the equation:

20 - 13 = n(A) + 13 - 5 - 13

7 = n(A) - 5

Then, we can add 5 to both sides of the equation to isolate n(A):

7 + 5 = n(A) - 5 + 5

12 = n(A)

Therefore, the cardinality of set A, n(A), is 12.