Explanation
To solve this problem, we need to calculate the actual number of people and then find the minimum (m) and maximum (n) possible values for the intersection (x).
1. Calculate the number of people in each set:
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Total Population, n(U)=200.
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People who like tea, n(T)=60% of 200=10060×200=120.
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People who like coffee, n(C)=72% of 200=10072×200=144.
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Since everyone likes either tea or coffee, n(T∪C)≤200.
2. Find the Minimum Intersection (m):
Using the set formula: n(T∪C)=n(T)+n(C)−n(T∩C).
To find the minimum intersection, we assume the union is at its maximum (200).
So, m=64.
3. Find the Maximum Intersection (n):
The intersection of two sets cannot be larger than the smaller set itself.
So, n=120.
4. Evaluate the Options:
We have m=64 and n=120. Let's check the difference:
Conclusion:
The value of n−m is 56, which matches option (A).
Correct Option:
(A) n−m=56
