Overlapping Sets

Question 1

Formulas

Answer 1

Only A + Only B + Both + Neither = Total

A + B - Both + Neither = Total

Question 2

3 group problems

Answer 2

If the number of elements belonging to exactly two of the groups not combined to a single sum (i.e. there is not mention of “exactly two in the question). then draw the circles and use:

Total = A only + B only + C only + A&B only + A&C only + B&C only + ABC + Neither

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

Total = A + B + C - (Groups of Exactly 2) - 2(Groups of Exactly 3) + Neither