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.