Solution to A group of students study at least one of the following subjects:biology, chemistry and physics. … - Sikademy
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Archangel Macsika

A group of students study at least one of the following subjects:biology, chemistry and physics. 36 of them study chemistry, 39 study biology and 41 study physics.15 study physics. 9 study all the three subjects. @draw a Venn diagram to illustrate this information.(b)from your diagram find:(1) the total number of students in the group.(2)the number of students who study only one [email protected] universal set U={2,3,5,7},p={2,5}and Q={5,7}find:(1)(PnQ),(2)P'UQ'. State the relationship between (1)and(2)(b)in a class of 50 students, 30 offer economics,17 offer government and 7 offer neither economics nor government. How many students offer both subjects.

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Here's the Solution to this Question

1.

(a)

N(C)=c+x+z+9

N(B)=b+x+y+9

N(P)=p+y+z+9

36 study chemistry:

c+x+z+9=36

39 study biology:


b+x+y+9=39

41 study physics


p+y+z+9=41

15 study only physics


p=15

There is not enough information to solve the problem.


2.

(a)


U=\{2,3,5,7\},P=\{2,5\},Q=\{5,7\}

(1)

(P\cap Q)=\{5\}

(2)

P'=\{3,7\}, Q'=\{2,3\}

(P'\cup Q')=\{2,3,7\}

(P\cap Q)=(P'\cup Q')'

(b)


N(E\cup G)=N(U)-N(E'\cap G')

=50-7=43

N(E\cup G)=N(E)+N(G)-N(E\cap G)

N(E\cap G)=30+17-43=4

4 students offer both subjects.


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