SOLUTION: If n(A) = 109, n(A ∪ B) = 140, and n(A ∩ B) = 44, find n(B).

Algebra.Com
Question 1067336: If
n(A) = 109, n(A ∪ B) = 140, and n(A ∩ B) = 44, find n(B).
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
If
n(A) = 109, n(A ∪ B) = 140, and n(A ∩ B) = 44, find n(B).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

There is a remarkable formula

n(A U B) = n(A) + n(B) - n(A ∩ B).


Regarding this formula, see the lesson 

    - Counting elements in sub-sets of a given finite set

in this site.


By applying the formula, you have 

140 = 109 + n(B) - 44,

and you get

n(B) = 140 - 109 + 44 = 75.


Answer.  n(B) = 75.

Solved.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Miscellaneous word problems".


RELATED QUESTIONS

If n(A)=15, n(B)=18, n(C)=16, n(A∩B)=7, n(A∩C)=6, n(B∩C)=7, and... (answered by ikleyn)
If n(B) = 17, n(A ∪ B) = 25, and n(A ∩ B) = 6, find... (answered by ewatrrr)
If n(A∪B)=40, n(A∩B)=10 and n(A)=15, find... (answered by Edwin McCravy)
If n(A) = 66, n(B) = 15, and n(A ∩ B) = 6, find n(A ∪ B). (answered by rothauserc,ikleyn)
If n(A∪B)=60 , n(A∩B)=20, and n(A)=n(B), find n(A) A. 10 B. 30 C. 40 D.... (answered by ikleyn)
If n(A∪B)=52,n(A∩B)=10, and n(A)=n(B), find n(A). A. 31 B. 21 C. 5 D.... (answered by ikleyn)
If n(A) = 102, n(A u B) = 140, and n(A ∩ B) = 41, find... (answered by MathLover1)
If n(A) = 5, n(A ∪ B) = 8, and n(B) = 5, then what is n(A ∩... (answered by MathLover1)
n(A) + n(B) = n(A ∪ B) + n(A ∩... (answered by solver91311)