A survey shows that 63% of the Americans like cheese whereas 76% like apples. If of the Americans like both cheese and apples, then we have:

Explanation: Solution 1. Define the Sets Let: : The set of Americans who like cheese. : The set of Americans who like apples. : The percentage who like both, so 2. Finding the Minimum Value of We know that the union of two sets cannot exceed the total population (100%): 3. Finding the Maximum Value of The number of people who like both ( ) cannot be greater than the number of people in the smaller individual set. Since and , the intersection cannot exceed the size of set : 4. Conclusion Combining both conditions: Correct Option: The correct option is (c) .

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