In a school, there are 68 teachers who teach Mathematics or Physics. Of these, 55 teach Mathematics and 45 teach both Physics and Mathematics. How many teach Physics?
58
Use \(n(M \cup P) = n(M) + n(P) - n(M \cap P)\).
Given \(n(M \cup P) = 68, n(M) = 55, n(M \cap P) = 45\).
\(68 = 55 + n(P) - 45 \Rightarrow n(P) = 68 - 10 = 58\)
Hence, the answer is 58.
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Important Questions from Union and Intersection of Sets
In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper I, 26 read newspaper T, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find the number of students who read exactly one newspaper.
If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A∪B) can have?
If A = {x : 0 ≤ x ≤ 2} and B = {y; y is a prime number}, then what is A ∩ B equal to?
Let A ∪ B = {x|(x - a)(x - b) > 0, where a < b}. What are A and B equal to?
Consider the following statements
1. A = (A ∪ B) ∪ (A - B),
2. A ∪ (B - A) = (A ∪ B)
3. B = (A ∪ B) - (A - B)
Which of the statements given above are correct?
