1.

Out of 25 members in a family, 12 like to take tea, 15 like to take coffee and 7 like to take coffee and tea both. How many like (i) at least one of the two drinks. (ii) only tea but not coffee, only coffee but not tea. (iv) neithertes nor cofee.

Answer»

Given that

n(T) = 12 

n(C)= 15 

n(T ∩ C) = 7 

(i)  n(T ∪ C) = n(T) + n(C) − n(T ∩ C) 

= 12 + 15 – 7 

n(T ∪ C) = 20 

20 members like at least one of the two drinks. 

(ii) Only tea but not coffee 

n(T) − n(T ∩ C) 

= 12 – 7 

= 5 

(iii) Only coffee but not tea 

= n(c) − n(T ∩ C) 

= 15 – 7 

= 8 

(iv) Neither tea nor coffee 

= n(u) − n(T ∪ C) 

= 25 – 20 

= 5

Given that n(T) = 12  

n(C)= 15  

n(T ∩ C) = 7  

(i)  n(T ∪ C) = n(T) + n(C) − n(T ∩ C)  = 12 + 15 – 7  n(T ∪ C) = 20

 20 members like at least one of the two drinks.  

(ii) Only tea but not coffee  n(T) − n(T ∩ C)  = 12 – 7  = 5  

(iii) Only coffee but not tea  = n(c) − n(T ∩ C)  = 15 – 7  = 8  

(iv) Neither tea nor coffee  = n(u) − n(T ∪ C)  = 25 – 20  = 5


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