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SETS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSETS2 Marks
Question
A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like product B, what is the least number that must have liked both products?
✓

Answer

Let U be the set of consumers questioned, S be the set of consumers who liked the product A and T be the set of consumers who like the product B.
Given that:
n(U) = 1000, n(S) = 720, n(T) = 450
Therefore, n(S $\cup$T) = n(S) + n(T) – n(S ∩ T)
= 720 + 450 – n (S ∩ T) = 1170 – n(S $\cup$T)
Thus, n(S $\cup$T) is maximum whenn(S $\cap$T) is least. But S $\cup$T $\subset$U implies
n(S $\cup$T) ≤ n ($\cup$) = 1000. So, maximum values of n(S $\cup$T) is 1000.
Therefore, the leastvalue of n(S $\cup$T) is 170.

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