Overlapping sets

Question 1

If A and B are two sets, what is the total # of unique elements?

Answer 1

Number of a only + number of b only + number of both + number of neither

OR

Number of a + number of b - number of both + number of neither

Question 2

What are the two options you could use to solve an overlapping set problem where percentages are involved and none of the numbers in the set are defined?

Answer 2

1) assume there are 100 items in the set

2) assign a variable to represent the total number of items in the set

Question 3

What are the two options you could use to solve an overlapping set problem where fractions are involved and none of the numbers in the set are defined?

Answer 3

1) assume that there are n items, where n is the LCM of the denominators of all the fractions
2) assign a variable to represent the total # of items in the two sets

Question 4

(A or B) =

Answer 4

(A or B) = #A + #B - #(A&B)

Question 5

Solving 3 circle Venn diagrams if the number of elements belonging to exactly 2 groups is not combined to a single sum- formula =

Answer 5

Total # of unique members = #(A only + B only + C only) + #((A&B) only + (A&C) only + (B&C) only) + #(A&B&C) + #(neither A nor B nor C)

Or

Total # of unique members = # in group A + # in group B + # in group C - # in (A&B) - # in (A&C) - # in (B&C) + # in triple overlaps + # in neither

Question 6

Solving 3 circle Venn diagrams if the number of elements belonging to exactly 2 groups is combined to a single sum- formula =

Answer 6

Total # of unique elements = # in (group A) + # in (Group B) + # in (Group C) - # in (Groups of Exactly Two) - 2(# in (Group of Exactly 3)) + # in (Neither)