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A group conducted a survey of 100 consumers and reported that 72 consumers like apples and 45 consumers like oranges, what is the least number that must have liked both products?

A group conducted a survey of 100 consumers and reported that 72 consumers like apples and 45 consumers like oranges, what is the least number that must have liked both products? Correct Answer 17

n(U)=100, n(A)=72, n(O)=45 n (A∪O) = n (A) + n (O) – n(A∩O) n (A∪O) ≤ n(U) => n (A∪O) ≤ 100 Greatest value of n (A∪O) is 100 which gives least value of n(A∩O) 100=72+45 – n(A∩O) n(A∩O) = 17 least value of n(A∩O).

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