Question

If nA=75%, nB=80%, nA∩B=350 and nA∪B=15%, find nU, the total number of elements.

Answer 1

Step-by-step explanation:

If n(a) =300, n(aub) =500, n(anb) =50, and n(b') =350, what is n(b) and n(u)?

It seems you are using identical symbols for different meanings, but what you intend seems clear from context. As I understand, the ‘u’ in ‘aub’ is set union, while a standalone ‘u’ as in n(u) is a universal set. Also it seems clear that the ’n’ in ‘n()’ is to be translated as ‘the number of elements in ()’, while in ‘anb’ you mean to indicate set intersection.

Start with n(aub) = n(a) + n(b) - n(anb). This formula holds because the sum n(a) + n(b) counts the elements in anb twice, so subtracting n(anb) once corrects the count.

n(aub) = n(a) + n(b) - n(anb)

500 = 300 + n(b) - 50

250 = n(b)

Also, assuming that you are indicating a set complement with an apostrophe, n(u) = n(b) + n(b’) = 250 + 350 = 600.