SOLUTION: I need help. There are 12 elements in the intersection of sets A and B, and there are 20 elements in the union of sets A and B. If set A has 4 fewer elements than set B, find the n

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Question 946496: I need help. There are 12 elements in the intersection of sets A and B, and there are 20 elements in the union of sets A and B. If set A has 4 fewer elements than set B, find the number of elements that are in set B, but not set A. Thanks.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the formula you need is:

number of elements in (A union B) is equal to numbers of elements in A plus number of elements in B minus number of elements in (A intersect B).

you are given that (A union B) is equal to 20.

you are given that (A intersect B) is equal to 12.

the formula becomes:

20 is equal to number of elements in A plus number of elements in B minus 12.

add 12 to both sides of this equation and you get:

32 is equal to number of elements in A plus number of elements in B.

you are given that the number of elements in A is 4 less than the number of elements in B.

this means that the number of elements in A is equal to the number of elements in B minus 4.

your equation of 32 is equal to number of elements in A plus number of elements in B becomes:

32 is equal to number of elements in B minus 4 plus number of elements in B.

add 4 to both sides of this equation and combine like terms to get:

36 is equal to two times the number of elements in B.

divide both sides of this equation by 2 to get:

18 is equal to the number of elements in B.

since A has 4 less, then the number of elements in A must be equal to 14.

your formula of:

(A union B) = A + B - (A intersect B) becomes:

20 = 14 + 18 - 12 which becomes:

20 = 20 which is true, confirming that the number of elements in A is equal to 14 and the number of elements in B is equal to 18.