Kenneth S. answered • 11/28/16

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Use a Venn diagram with three circles partially overlapping. Begin by placing the number 3 in that area which is common to all three circles. Then use subtraction to compute what number goes into the rest of these three regions:

intersection of Spanish & French

intersection of French & German

intersection of Spanish and German.

Get the idea? Consult examples like this that there must be in your class textbook and/or lecture notes, etc.

Kenneth S.

The circle representing Spanish consists of four parts:

3 in the intersection of all 3 circles

3 in the part where French & Spanish are recorded, NOT COUNTING the 3 that takes all 3 languages

4 in the part where Spanish and German are recorded NOT COUNTING the 3 that takes all 3 languages.

So far, that is 14 persons, therefore the remaining part, Spanish only, must be 14.

Similarly, French only should be 17, German only should be 20, French and German (but not all 3) is 1, and altogether that is 62 persons. Therefore 5 took none of these languages.

To summarize, you have to be sure not to "double count" anyone.

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11/28/16

Jason H.

11/28/16