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.

Explanation

To find how many students were taking neither apple juice nor orange juice, we can use the principle of inclusion-exclusion. Here’s a step-by-step solution:

### Step 1: Define the Variables
Let:
- \( N \) = Total number of students surveyed = 400
- \( N(A) \) = Number of students taking apple juice = 100
- \( N(O) \) = Number of students taking orange juice = 150
- \( N(A \cap O) \) = Number of students taking both apple and orange juice = 75
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