Question

in a class of 42 students is play at least one of 3 game cricket hockey and football it is a found at 14 play cricket 20 play hockey 24 play football 3 play Both cricket and football to play both hockey and football and play all the three games find the number of student who play cricket but not only hockey ​

Answer 1

Answer:

Let the set of students who play cricket, hockey and football be C, H, F respectively.

Then,

n(C) = 14, n(H) = 20, n(F) = 24, n(C intersection F) = 3, n (H intersection F) = 2, n (C union H union F) = 42  and n (C intersection H intersection F) = 0.

 

We know:

n (C union H union F) = n(C) + n(H) + n(F) - n(C intersection H) - n(H intersection F) - n(C intersection F) + n (C intersection H intersection F)

 

Substituting the values, we get,

n(C intersection H) = 11

 

But, C = (C intersection H) intersection (C union H')

So, n (C) = n (C intersection H) + n (C intersection H')  

 

[Since, (C intersection H) and (C intersection H') are disjoint sets]

 

Substituting the values, we get

n (C intersection H') = 3

 

Thus, the number of students who play cricket but not hockey is 3.

Step-by-step explanation:

Answer 2

Answer:

3

Step-by-step explanation:

Let the set of students who play cricket, hockey and football be C, H, F respectively.

Then,

n(C) = 14, n(H) = 20, n(F) = 24, n(C intersection F) = 3, n (H intersection F) = 2, n (C union H union F) = 42  and n (C intersection H intersection F) = 0.

Also,

n (C union H union F) = n(C) + n(H) + n(F) - n(C intersection H) - n(H intersection F) - n(C intersection F) + n (C intersection H intersection F)

Substituting the values, we get,

n(C intersection H) = 11

But, C = (C intersection H) intersection (C union H')

So, n (C) = n (C intersection H) + n (C intersection H')  

[Since, (C intersection H) and (C intersection H') are disjoint sets]

Substituting the values, we get

n (C intersection H') = 3

Thus, the number of students who play cricket but not hockey is 3.

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https://brainly.in/question/7196394

https://brainly.in/question/5065639

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