Overlapping Sets

Question 1

Basic overlapping set problem

Answer 1

(A or B) = #(A) + #(B) - #(A and B/BOTH)

Question 2

Formula for overlapping set of 3 [equation]

Answer 2

• If the number of elements belonging to exactly two of the groups is combined to a single sum (i.e. the problem is giving us the number of elements belonging to “exactly two” of the groups), such as in the previous two problems, then we use the following formula:

Total # of Unique Elements = # in (Group A) + # in (Group B) + # in (Group C) – # in (Groups of Exactly Two) – 2 [#in (Group of Exactly Three)] + # in (Neither)

Question 3

Formula for overlapping set of 3 [venn diagram

Answer 3

• If the number of elements belonging to exactly two of the groups is combined to a single sum (i.e. there is no mention of “exactly two” in the question), such as we saw in the ”rock star question” from the previous lesson, then we draw out the circles and use the formula:

Total # of Unique Elements = # in (Group A) Only + # in (Group B) Only + # in (Group C) Only + # in (Double Overlaps) Only + # in Triple Overlap + # in Neither