Overlapping Sets

Question 1

Set matrix

Answer 1

Question 2

what are some unique formulas that arise when dealing with overlap of TWO sets A, and B

Answer 2

1) total number of unique elements in the set = (# only A) + (# only B) + (neither A or B) + (both A & B)
2) total # unique elements in the set = (# A) + (#B) - (both A & B) + (neither A or B)

Question 3

how do we deal with cases where the number of items in a set are not given, and instead are represented as a % of the total?

Answer 3

1) either assume the total number of items is 100
2) assign a variable to represent the total number of items in set

Question 4

how do we deal with cases where the number of items are represented in fractional form instead of given explicitly or represented as a percent?

Answer 4

1) let the total be the LCM of all the fraction denominators
2) let the total be some variable

Question 5

if some of the item numbers are actually defined as opposed to being percents or fractions of the total, how do we do our calculations?

Answer 5

have to base them off the total number - cant use notional “100” total for percents or LCM of denominators for fractions

Question 6

when algebra is required in setting up overlapping set matrix…

Answer 6

pay very careful attention to language describing amounts of each item so you don’t mess up

Question 7

what do we need to determine the number of elements belonging to exactly one group?

Answer 7

values for the total, both, and neither

Question 8

what is the formula for finding the number of members in either set A or set B?

Answer 8

members in either A or B = (# in A only) + (# in B only) + (# in both A and B)

Question 9

how do you determine the total number of members in either set A or B when you are given total number of items in set A and B?

Answer 9

members in either A or B = total in A + total in B - # items in both A and B

Question 10

three set overlap venn diagram

Answer 10

Question 11

whenever there is an overlap in sets A and B, what is the problem with assuming that the sum of the members of groups A and B is the total number of members?

Answer 11

since there are some members part of both groups, it double counts

Question 12

another screenshot

Answer 12

the number of elements in the entire Group A circle represent the total number of elements that belong to group A, same for groups B and C

Question 13

in A only + # in B only + # in C only = ?

Answer 13

number of elements with the three sets that belong to only one group

Question 14

in any X and Y region (overlap in venn diagram of sets X and Y) there will also be elements of Z (from the portion of the overlap in the very center that contains the intersection of X and Y and Z

Answer 14

this means that saying the venn diagram region of “X and Y” is not equivelant to saying “X and Y only”

Question 15

number in A & B only =?

Answer 15

(number in A and B) - (number in A, B, and C only)

Question 16

the total number of unique elements in a group is the sum of all the elements belonging to exactly one group, all the elements belonging to exactly two groups, all the elements belong to exactly three groups, and all the elements belonging to none of the groups - represented as the sum of all the variables in the following screenshot

Answer 16

Question 17

when filling out a venn diagram, always start with the regions of the most overlap so that you can deduct that region from what you will out afterwards

Question 18

What formula do you use if you:
1) are given the sum of the X and Y only region (the double overlap region)
2) are asked to find the sum of the X and Y regions
* note the - 2*[# in exactly three groups]

Answer 18

Question 19

review 13.4.2 and 13.4.3…. theyre tough

Question 20

if you are trying to find the number of elements not in any of the groups and you have your three part diagram filled out in all overlap spots, how do you quickly finish problem?

Answer 20

take the total minus the sum of all the elements of the three main circles, and that is your null group