Ayuda?

Respuesta :

T = { Socios de club deportivo }

A = { Socios que practican fútbol }

B = { Socios que practican basquet }

C = { Socios que practican tenis }

n(T) = 85

n(A) = 43

n(B) = 46

n(C) = 41

Como es un club deportivo todos los socios

se dedican a la practica del deporte :

n(A∪ B∪ C) = n(T)

n(A∪ B∪ C) = 85

Socios que practican solo un deporte :

n(A - (B∪ C)) + n(B - (A∪ C)) + n(C - (A∪ B)) = 45

Socios que practican tres deportes :

n(A∩ B∩ C) = 5

Socios que practican solo dosdeportes :

n(A ∩ B - C) + n(A∩ C - B) + n(B∩ C - A) = x

Según Diagrama de Venn :

n(A - (B∪ C)) = a

n(B - (A∪ C)) = c

n(C - (A∪ B)) = f

n(A - (B∪ C)) + n(B - (A∪ C)) + n(C - (A∪ B)) = 45

a + c + f = 45

n(A ∩ B - C) = b

n(A∩ C - B) = d

n(B∩ C - A) = e

n(A ∩ B - C) + n(A∩ C - B) + n(B∩ C - A) = x

b + d + e = x

n(A∪ B∪ C) = a + b + c + d + e + f + 5

85 = a + c + f + b + d + e + 5

85 = 45 + x + 5

85 = 50 + x

85 - 50 = x

35 = x

x = 35.