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A survey was given to 339 people asking whether people like dogs and/or cats.

190 said they like dogs
141 said they like cats
88 said they don't like cats or dogs.

How many said they liked both cats and dogs?

Respuesta :

aramisdegaula1977

Answer:

80.

Step-by-step explanation:

Let [tex]C[/tex] be the set of people who like cats and [tex]D[/tex] the set of people who like dogs. Under the cardinality theorem you have

n(CUD) = n(C) + n(D) - n(CnD)[/tex], isolating the [tex](C[/tex]∩[tex](D[/tex] , you have n[tex](C[/tex]∩[tex](D[/tex]  = n(C) + n(D) - [tex](C[/tex]∪[tex].

As a total of 339 individuals, and 88 are those who do not like cats or dogs, then 251 of them are those who like cats or dogs. Then, n[tex](C[/tex]∩[tex](D[/tex]  [tex]= 190 +141 -251 = 80[/tex]