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

(i) Set C contains letters of word 'cooler' — c, o, l, e, r.

C = {c, o, l, e, r}

(ii) n(C) is the cardinal number of set C.

n(C) = 5

(iii) Here the set has 5 elements, the number of subsets = 2⁵ = 2 x 2 x 2 x 2 x 2 = 32.

Number of subsets of B are 32.

(iv) Here the set has 5 elements, the number of subsets = 2⁵ - 1 = 2 x 2 x 2 x 2 x 2 - 1 = 32 - 1 = 31.

Number of proper subsets of B are 31.