In a survey of 400 students in a school, 100 were listed as taking app

1.	In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.
Answer» Let U = set of surveyed students A = set of students taking apple juice B = set of students taking orange juice. Then n(∪) = 400; n(A) = 100; n(B) = 150; and n(A∩B) = 75 Now n(A’∩B’) = n(A∪B)’ = n(∪) – n(A∪B) = n(∪)-n(A)-n(B) + n(A∩S) = 400-100-150 + 75 = 225 ∴ 225 students were taking neither apple juice nor orange juice.

In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

Answer»

Let U = set of surveyed students

A = set of students taking apple juice

B = set of students taking orange juice.

Then n(∪) = 400; n(A) = 100; n(B) = 150; and n(A∩B) = 75

Now n(A’∩B’) = n(A∪B)’

= n(∪) – n(A∪B)

= n(∪)-n(A)-n(B) + n(A∩S)

= 400-100-150 + 75 = 225

∴ 225 students were taking neither apple juice nor orange juice.