contestada

Find, if possible, the number of elements in sets A, B and C using the given information. If there is an inconsistency, state where it occurs. An B= 0, n(A n C) = 10, n(B n C) = 1, n(C - A) = 9, n(A - C) = 12, n(U) = 31

Respuesta :

Using Venn sets, the number of elements in the sets are given as follows:

  • Set A: 22.
  • Set B: 1.
  • Set C: 19.

What are the Venn Sets?

For this problem, we consider that the sets A, B and C are the sets represented in the problem, and use the information given to find the number of elements in each set.

For the set A, we have that:

  • n(AnB) = 0
  • n(A n C) = 10.
  • n(A - C) = 12,

Hence 12 elements belong only to set A and 10 belong to both A and C, hence set A has 22 elements.

For the set B, we have that:

  • n(AnB) = 0
  • n(B n C) = 1

In total, there are 31 elements, of which:

  • 12 are only in A.
  • 9 are only in C.
  • 10 are in both.

31 - 31 = 0, hence set B has only 1 element, that is also present in set C.

For the set C, we have that:

  • n(B n C) = 1.
  • n(C - A) = 9.
  • n(A n C) = 10

Hence it has 10 elements that are also in set A, and 9(the intersection with B is included in C - A as n(AnB) = 0) are not, hence set C has 19 elements.

More can be learned about Venn sets at brainly.com/question/24388608

#SPJ1