Question

If S and T are sets such that n(S x T)=15, n(S) = 3, and n(S ∪ T)=6, find n(S ∩ T).

Answer 1

Answer: 2

Reason

n(S x T)=15 tells us there are 15 ordered pairs in the set S x T.

Each ordered pair is of the form (m,n) where m is in set S, and n is in set T.

This is the cross product of set S and set T.

Because n(S) = 3, we then can know n(T) = n(S x T)/n(S) = 15/3 = 5

This is because n(S x T) = n(S)*n(T)

The x refers to the cross product set operation while the asterisk is the multiplication symbol. The two ideas are somewhat related but not exactly the same thing.

We then have these steps

n(S ∩ T) = n(S) + n(T) - n(S ∪ T)

n(S ∩ T) = 3 + 5 - 6

n(S ∩ T) = 2