Answer
$A'∩ B = 10$
$A\cup B = 92$
Work Step by Step
a)
$A = 80 +2 = 82$, the sample with excellent surface finish
$B = 80 + 10 = 90$, the sample with excellent edge finish
$A'$ include samples with good surface finish = Total parts - samples with excellent surface finish
$A' = 100 - A = 100 - 82 = 18$
$B'$ include samples with good edge finish = Total parts - samples with excellent edge surface finish
$B' = 100 - B = 100 - 90 = 10$
$A'\cap B$ include samples with good surface finish and excellent edge finish. From the given data, only 10 samples fit this criterion.
$A'\cap B = 10$
By the property of union of sets, $n(A\cup B)=n(A) +n(B) - n(A\cap B)$
$n(A\cup B) = 82+90-80$
$n(A\cup B)= 92$
