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in Sets, Relations and Functions by (26.1k points)
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In a Survey of 450 people, it was found that 110 play cricket, 160 play tennis and 70 play both cricket as well tennis. How many play neither cricket nor tennis?

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Best answer

Let C and T denotes the students who play cricket and tennis, respectively. 

Given

n(c) = 110, n(T) = 160, n(C ∩ T) = 70, n(u) = 450. 

Using identity

n(C ∪ T) = n(C) + n(T) − n(C ∩ T) 

= 110 + 160 – 70 

= 200 

∴ No, of students play neither cricket nor tennis 

n(u) − n(C ∩ T) 

= 450 – 200 

= 250

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