Question 1191782
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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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<pre>
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.
</pre>

Solved and explained.


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To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

in this site.


Learn the subject from there.