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Example 26 - In a survey of 400 students in a school, 100 apple - Number of elements in set  - 2 sets - (Using properties)

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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Example 26, 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 and orange juice . How many students were taking neither apple juice nor orange juice. Let A, O denote the set of students taking apple juice & orange juice respectively, Number of students who take apple juice = n(A) = 100 Number of students who take orange juice = n(O) = 150 Number of students who take both orange juice and apple juice = n(O ∩ A) = 75 n (A ∪ O) = n (A) + n (O) – n (A ∩ O) = 100 + 150 – 75 = 175 So, Number of students who take either apple or orange juice = 175 Number of students who take neither apple juice not orange juice = Total number of students – Number of students who like either apple juice or orange juice = 400 – 175 = 225 Hence 225 students were taking neither apple juice nor orange juice.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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