(GAte[Discrete Mathematics] and other comp Exam) In a group of 26 people , 8 take tea

Question

In a group of 26 people , 8 take tea but not coffee and 16 take tea.How many take coffee but not tea ?

Answer 1

Let A=People who takes Tea

B=People who takes Coffee

A U B =26

A-B={8}

n(A) = n( A - B ) + n( A ∩ B )

16 = 8 +  n( A ∩ B )

 n( A ∩ B ) = 8

n(A ∪ B) = n( A - B ) + n( A ∩ B )+ n( B - A )

26 = 8 + 8 + n( B - A )

n( B - A ) =10

Hence Number of people who take coffee but not tea = 10