Question

n(A)= 48, n(A')=40, n(B')=74 U= a universal set
u= union.
Find the number of elements in A u B.
n(A u B)=_____________________________?

Answer 1

Use
\[A \cup A' = U\]
and
\[B \cup B' = U\]
=>
n(U)=n(A)+n(A')=48+40=88
and
n(U)=n(B)+n(B')=88
n(B)=88-n(B')=88-74=14

\[n(A \cup B) = n(A)+n(B)-n(A \cap B)\]
\[=48+14-n(A \cap B)\]
\[=62 - n(A \cap B)\]

We cannot calculate a numerical value since the intersection of A and B is not known.