In a class of 80 students, 53 study Art, 60 study Biology, 36 study Art and Biology, 34 study Art and Chemistry, 6 study Biology only and 18 study Biology but not Chemistry. Illustrate the information on a Venn diagram. Determine the number of students who study
(I) Arts only
(ii) Chemistry

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  1. Did you sketch your Venn diagram?

    The missing part is the intersection of all 3, label it x
    Now look at the intersection of A and C, it must be 34.
    But you already have x accounted for in the intersection of all 3.
    So label the part in A and C, but not B as 34-x

    36 study A and B, so the part of A and B, but not C is

    Given that 53 study Art, in the A only part we can put
    53-(36-x) - (34-x) -x = x - 17

    6 study B only, put that in.

    So the missing part of B is 60 - 6 - (36-x) - x
    = 18

    18 study B , but not C, so they could be in A
    label the part of A and B, but not C as 18

    BUT, we already know that A and B, not C, is 36-x
    So 36-x = 18

    I think we are done
    Finish circle A, with A only as x-17 or 18-17 = 1
    Replace the other values.

    We still are missing the C only part.
    But we know that the total of all the parts is 80
    By simple subtraction, the C only part is 3

    Check by verifying each part with the given information.

    Arts only is 1
    Chemistry is 55

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  2. Solution

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  3. what will be both chemistry and biology?

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  4. 1 and 55

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  5. I want diagram

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  6. Arts only = 1
    Chemistry = 55
    Both biology and chemistry is 0

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  7. Please I need a venn diagram for this question

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  8. Art only should be 7 but not 1.

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  9. art only should be 7 and chemistry is 55 according to akiola from answers given

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  10. Mr Kwame's mistake was the place to find the value of x.

    Biology but not chemistry means that, biology only plus the intersection of biology and Art.

    So it should have been 6 +36-x=18. It means x=24.

    So the value of all the intersections of the regions is 24.

    Finishing circle A, with A only as x-17 or 24-17 = 7.

    Let q denote the intersection of biology and chemistry only.
    So 60-(36-x +x+6)= q.
    > 60-(36-24+24+6)=q
    = 60-42=q

    Therefore q = 18. Get it ?

    We are still missing the C only part.

    But we know that the total of all the parts is 80.
    So to calculate for only C part,
    80- (10+7+12+24+6+18)=y(i.e C only).
    So y= 3. Thus only C is 3.

    Those who study chemistry = 10+24+18+3=55.

    From our working:
    Arts only is 7 and

    Chemistry is 55.

    So akiola answer is correct.

    I could have given you the venn diagram but I am using mobile device so I cannot give you the venn diagram.

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  11. Correct!!!

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  12. Sorry, Mr. Reiny rather not Mr. Kwame.Trial; In a class of 70 students, 6 offer Economics only, 18 offer Economics but not Mathematics, 36 offer Economics and Geography, 53 offer Economics, 50 offer Geography and 34 offer Mathematics and Geography. All students offer at least one subject. Determine the number of students who offer: (1)mathematics (2)mathematics and geography but not economics.

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  13. Thanks for letting me understand

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  14. Excellent work

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