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in Mathematics by (54.6k points)

If C is the set of letters in the word “cooler”, find : 

(i) Set C 

(ii) n(C) 

(iii) Number of its subsets 

(iv) Number of its proper subsets.

Note : (i) If a set has n elements, the number of its subsets = 2n 

(ii) If a set has n elements, the number of its proper subsets = 2n – 1

1 Answer

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(i) C = {c, o, l, e, r} 

(ii) n(C) = 5 

(iii) Number of its subsets : 25= 2 x 2 x 2 x 2 x 2 = 32 

(iv) Number of its proper subsets = 25 – 1 = 32 – 1 = 31

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