Use the union rule to answer the question: If n(B)=36, n(A∩B)=7 & n(A∪B)=63; what is n(A)?

Question

This is a Finite Math Question

Answer 1

n (A∪B) = n(A) + n(B) - n(A∩B)
n (A)= n (A∪B) + n(A∩B) - n(B)
n(A) = 63 + 7 - 36
n(A) = 70 -36
n(A) = 34

Answer 2

We have that (A AND B)=7 and (A OR B)=63; this means that there are 63 "items" that belong to at least one of A or B, and 7 of those "items" belong to both.

So, we can use this formula:
n(A OR B) = n(A) + n(B) - N(A AND B)
63 = n(a) + 36 - 7
63 = n(a) + 29
n(a) = 34

Answer 3

n(A U B) = n(A) + n(B) - n(A ∩ B)
So
63 = n(A) + 36 -7 = n(A) + 29.
Thus n(A) = 34.