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April 10th, 2018, 12:50 PM   #1
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Question How do I find the number of elements in differents sets when the total is not given?

The problem is as follows:

In an institution they offer three language courses one being German, the other French and the last one Polish. Four students enrolled in the three courses, six students in Polish and German and seven in French or Polish. If all students enrolled in Polish also enrolled in German or French. How many of the students were in the Polish course?

The existing alternatives in my book are:
  • 9
  • 7
  • 6
  • 5
  • 8

What I tried to do is to build up a Venn diagram as shown in the attachments:

But from this point I am stuck as I do not know how to relate the number of students in Polish language since there is not known the total number of elements from all sets together.

Can this problem be solved without needing this information?.

There is one thing regarding how I understood the problem as it mentions *seven students enrolled in French or Polish* so by interpreting this information I assumed that $P=7$ and $F=7$ therefore the diagram would become into the second figure attached.

But I'm not sure if this is the right way to solve this problem neither if my "solution" is correct.

Therefore I'm stuck at this, can somebody help me to go in the right track or point out where did I misunderstood things?
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File Type: png problem_09042018_03.png (16.5 KB, 0 views)
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April 10th, 2018, 01:14 PM   #2
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April 10th, 2018, 01:21 PM   #3
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There seems t be some ambiguity in the statement "seven in French or Polish". Does this mean French or Polish alone or seven in French and possibly others and seven in Polish and possibly others?
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April 10th, 2018, 02:21 PM   #4
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There seems t be some ambiguity in the statement "seven in French or Polish". Does this mean French or Polish alone or seven in French and possibly others and seven in Polish and possibly others?
There is an error in the way how I transcribed the problem from my book. It should have said "French and Polish". I'm going to edit this.
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April 10th, 2018, 02:24 PM   #5
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Why do we have to conclude that there no elements in $P$ alone?. This part is where I'm stuck at. Is it because we have not filled out the other spaces so by this we conclude there aren't any students there?

Can you please help me to understand?.
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April 10th, 2018, 03:33 PM   #6
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Why do we have to conclude that there no elements in $P$ alone?. This part is where I'm stuck at. Is it because we have not filled out the other spaces so by this we conclude there aren't any students there?

Can you please help me to understand?.
It says directly all students enrolled in Polish are also enrolled in German or French. Thus there are no students enrolled only in Polish.
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April 11th, 2018, 09:24 AM   #7
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It says directly all students enrolled in Polish are also enrolled in German or French. Thus there are no students enrolled only in Polish.
Yay! I totally failed to notice that part. Out of curiosity, which software did you used to make those diagrams?.
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April 11th, 2018, 09:49 AM   #8
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Yay! I totally failed to notice that part. Out of curiosity, which software did you used to make those diagrams?.
powerpoint

Once upon a time I had Visio and loved it but the new version is too pricey.
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