SOLUTION: Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in
Algebra.Com
Question 1047234: Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in set A?
Found 3 solutions by stanbon, ikleyn, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in set A?
-----
A + B - (A and B) = (A or B)
-----
A + 61 - 38 = 112
------
A = 150-61
----
A = 89 elements
---------------------
Cheers,
Stan H.
----------------
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
See the lesson
- Counting elements in sub-sets of a given finite set
in this site.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
RELATED QUESTIONS
Suppose Set A contains 87 elements and Set B contains 30 elements. If Sets A and B have... (answered by stanbon)
Suppose Set A contains 66 elements and Set B contains 94 elements. If Sets A and B have 1 (answered by mananth,jim_thompson5910,ikleyn)
Suppose Set A contains 60 elements and the total number elements in either Set A or Set B (answered by ikleyn)
I need help, I can't seem to understand this problem
Suppose Set A contains 84... (answered by ikleyn)
Suppose Set B contains 69 elements and the total number elements in either Set A or Set B (answered by MathLover1)
Suppose set A contains 86 ELEMENTS and the total number ELEMENTS in either Set A or Set B (answered by Theo)
The set A union B has 26 elements. Set A contains 15 elements, and set B contains 17... (answered by stanbon)
If Set A has 9 letters and 3 numbers. Set B has 12 letters and 1 number. 9 letters and... (answered by Edwin McCravy)
I need help. There are 12 elements in the intersection of sets A and B, and there are 20... (answered by Theo)