in a class of 60 students 30 like maths 25 like physics 30 like chemistry. if 10 like both physics and maths 5 like maths and chem and 5 like phy & chem and 3 like all the subjects. find student like none of subject if 100 students were surveyed
It is a common problem in set theory, however, it is not so common in a class of 60 students, 100 of them were surveyed.
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To solve this problem, we can use the principle of inclusion-exclusion.
Given:
Total students surveyed (n) = 100
Number of students who like Maths (A) = 30
Number of students who like Physics (B) = 25
Number of students who like Chemistry (C) = 30
Number of students who like both Maths and Physics (A ∩ B) = 10
Number of students who like both Maths and Chemistry (A ∩ C) = 5
Number of students who like both Physics and Chemistry (B ∩ C) = 5
Number of students who like all three subjects (A ∩ B ∩ C) = 3
To find the number of students who like none of the subjects, we need to subtract the total number of students who like at least one subject from the total number of students surveyed.
Step 1: Find the number of students who like at least one subject (A ∪ B ∪ C):
(A ∪ B ∪ C) = (A + B + C) - (A ∩ B + A ∩ C + B ∩ C) + (A ∩ B ∩ C)
= (30 + 25 + 30) - (10 + 5 + 5) + 3
= 110 - 20 + 3
= 93
Step 2: Find the number of students who like none of the subjects:
Number of students who like none of the subjects = n - (A ∪ B ∪ C)
= 100 - 93
= 7
Therefore, there are 7 students who like none of the subjects.