Question 1047234
set B contains 61 elements.
total number of elements in set A or set B is 112.
sets A and B have 38 element in common.


the formula is number of elements in set (A or B)  is equal to the numbers of elements in set A plus the number of elements in set B minus the elements that are in both set A and set B.


the formula assumes that the elements in set A include the elements that are also in set B, and it assumes that the elements in set B include the elements that are also in set A.


because of this, the elements in set A and B are double counted, once as part of set A and again as part of set B.


the subtraction of the number of elements in both set A and B eliminates the double counting.


you get:


112 = 61 + A - 38


A represents the number of elements in set A


solve for A to get A = 112 - 61 + 38 = 89


there are 61 elements in set A and 89 elements in set B.


each set is assumed to contain elements that are in both.


take out the elements in set A that are also in set B.
take out the elements in set B that are also in set A.


you get the number of elements in set A only are 61 - 38 = 23.
you get the number of elements in set B only are 89 - 38 = 51.


now count the number of elements that are in both set A and B separately.


you get 23 in A and 51 in B and 38 in both for a total of 112.