Question

An a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of
the two drinks. How many people like both coffee and tea? ☕​

Answer 1

Step-by-step explanation:

Let C denote the set of people who like coffee, and T denote the set of people who like tea

n(C∪T)=70,n(C)=37,n(T)=52

We know that:

n(C∪T)=n(C)+n(T)−n(C∩T)

∴70=37+52−n(C∩T)

⇒70=89−n(C∩T)

⇒n(C∩T)=89−70=19

Thus, 19 people like both coffee and tea

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Answer 2

$\huge\bf\mathfrak\blue{✫}$$\huge\bf\mathfrak{Required\: Answer}$

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19 people like both Tea and Coffee.

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• Let c be the set of people who like coffee.
• Let T be the set of people who like Tea.

$\bf\underline\mathcal\blue{Given}$

• Total number of people, n(T U C) = 70
• Number of people who like coffee, n (C) = 37
• Number of people who like Tea, n(T) = 52

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$\bf\underline\mathcal\blue{Using\: Formula :}$

n ( T U C) = n( T ) + n(C) - n(T U C)

Substituting the values:

70 = 52 + 37 - n(T U C)

70 = 89 - n( T U C )

n ( T U C ) = 89 - 70

⁂ n ( T ∩ C ) = 19.

Thus, 19 people like both Tea and Coffee.

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