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.