Let A – Apple juice; O – Orange juice be the sets.
Given; n(U) = 400; n(A) = 100;
n(O) = 150; n(A ∩ O) = 75
n (neither apple juice nor orange juice)
= n(A’ ∩ O’) = n((A ∪ O)’)
= n(U) – n(A ∪ O)
= 400 – [n(A) + n(O) – n(A ∩ O)]
= 400 – [100 + 150 – 75]
= 400 – 175 = 225.