Question 1053404
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Seventy tourists out of a group of 100 speak German 45 speak French and 23 speak both German and French. 
How many tourists in the same group speak neither German or French. Use set notations
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<pre>
Let G be the set of tourists speaking German, and n(G) is the number of people in this set ( n(G) = 70 ).

Let F be the set of tourists speaking French, and n(F) is the number of people in this set ( n(F) = 45 ).

Let FnG be the intersection of F and G. n(FnG) = 23.

Then the number of those who speal German OR French is the union of F and G and

n(F U G) = n(F) + n(G) - n(FnG) = 70 + 45 - 23 = 92.

Then the number of those who speaks neither German or French is 100 - 92 = 8.

<U>Answer</U>. 8.
</pre>

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.


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 textbook under the topic <U>"Miscellaneous word problems</U>".