SOLUTION: 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

Question 1053404: 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
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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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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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.

Answer. 8.

See the lesson
- Counting elements in sub-sets of a given finite set
in this site.

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 textbook under the topic "Miscellaneous word problems".

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