Question

(i) If the number of proper subsets of a set is 63 , find the

number of elements in the set . [2]

(ii) If A = { a , b, c }, then write the power set P(A). [1]​

Answer 1

Answer:

(i) number of elements = 64

(ii) P(A) = 8

Step-by-step explanation:

i) the no. of proper subset = 63

 no. of element = ?

 proper subset = 2^n - 1 ( n= no. of element in the set)

                 63 = 2^n -1

                 63 + 1 = 2^n

                  64 = 2^n

equating the powers,

2^6 = 64

i.e n = 6

number of elements in the set = 6

ii) A= {a,b,c}

power set = { { } , {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c} }

to check: P(A) = 2^n

                        = 2^3 ( n = number of elements)

                        = 8