Mathematics
In a class of 40 students, each one plays either Tennis or Badminton or both. If 28 play Tennis and 26 play Badminton, find
(i) how many play both the games;
(ii) how many play Tennis only;
(iii) how many play Badminton only.
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Answer
Given:
Total students in the class: n(T ∪ B) = 40
Students who play Tennis: n(T) = 28
Students who play Badminton: n(B) = 26
(i) how many play both the games
This represents the intersection of the two sets, n(T ∩ B).
We use the formula:
n(T ∩ B) = n(T) + n(B) - n(T ∪ B)
Substituting the values in above, we get:
n(T ∩ B) = 28 + 26 - 40
n(T ∩ B) = 54 - 40
n(T ∩ B) = 14
∴ 14 students play both the games.
(ii) how many play Tennis only
This represents the set T - B, consisting of students who play Tennis but do not play Badminton.
We use the formula:
n(T - B) = n(T) - n(T ∩ B)
Substituting the values in above, we get:
n(T - B) = 28 - 14
n(T - B) = 14
∴ 14 students play Tennis only.
(iii) how many play Badminton only
This represents the set B - T, consisting of students who play Badminton but do not play Tennis.
We use the formula:
n(B - T) = n(B) - n(T ∩ B)
Substituting the values in above, we get:
n(B - T) = 26 - 14
n(B - T) = 12
∴ 12 students play Badminton only.
The Venn diagram is shown below:
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