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a) Vann (Venn) diagramm - is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. This lends to easily read visualizations; for example, the set of all elements that are members of both sets S and T, S ∩ T, is represented visually by the area of overlap of the regions S and T. In Venn diagrams the curves are overlapped in every possible way, showing all possible relations between the sets.

2 students study only biology, because "half as many students who study chemistry only study biology only",half of 4 is 2.

"one third of the students who study biology study all there subjects", 21 * (1/3) = 7 students who study biology study all there subjects

"study chemistry are 5 more than those who study agric" : 20+5=25 study chemistry.

"twice as many students who study exactly one of the subjects study 2 of the 3 subjects"

3 + 4 + 2 =9, 9*2=18

"who study exactly one of the subjects study 2 of the 3 subjects" - chemistry and biology (z) or chemistry and agrik (y) or agrik and biology (x)

Let x,y,z - number.

(II) x+y+z=18=9*2=(3 + 4 + 2)*2

3+x+y+7=20

x+y=10

y+z+7+4=25

y+z=14

x+z+7+2=21

x+z=12

=> because x+y+z=18, (x+y)+z=18

z=8

x+(y+z)=18

x=4

y+(x+z)=18

y=6

"number of students who study agric and chemistry only is equal to the (IV)number of students who do not study any of the 3 subjects."

(IV)"agric and chemistry only " is "y" = 6

b) Class=3+2+4+4+6+8+6+7=40

(III) is "(IV) + only most one subject"

(III) 6+3+2+4=15

(II) study at least 2 subjects" is all (three) or two subject

all: 7

two: x+y+z=18

18+7=25