Question 1067336
.
If
n(A) = 109, n(A ∪ B) = 140, and n(A ∩ B) = 44, find n(B).
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<pre>
There is a remarkable formula

n(A U B) = n(A) + n(B) - n(A &#8745; B).


Regarding this formula, see the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

in this site.


By applying the formula, you have 

140 = 109 + n(B) - 44,

and you get

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


<U>Answer</U>.  n(B) = 75.
</pre>

Solved.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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