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Each of the 40 boys in a group plays at least one of the two games: Badminton(B) and
Football(F). 21 play Badminton and 28 play Football. Let the number of boys who play both
Badminton and Football be x.
a. Draw a clearly labelled Venn diagram to illustrate this information.
b.Hence, find
i.The value of x,
ii.The number of boys who play only Badminton but not Football.
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Use the fundamental formula for the union of two subsets B and F of the given finite set
n(B U F) = n(B) + n(F) - n(B ∩ F).
In your case, n(B U F) = 40, since each of the 40 boys in a group plays at least one of the two games,
and x = n(B ∩ F).
Therefore, 40 = 21 + 28 - x, which implies
x = 21 + 28 - 40 = 49 - 40 = 9.
Thus 9 boys play both sports.
The number of those who play only Badminton, is 21 - 9 = 12.
To get it, we should subtract those who play both sports from those who play Badminton.
Solved and explained.
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To see many other similar (and different) solved problems, look into the lesson
- Counting elements in sub-sets of a given finite set
in this site.
Learn the subject from there.