Question

let the set a be defined as follows.
a = {47, 41, 31, 17, 13, 11}
(a) find the total number of proper subsets of a.

(b) find the total number of subsets of a.

Explanation:

Step1: Count elements in set A

$n = |A| = 6$

Step2: Calculate total subsets

Total subsets = $2^n = 2^6 = 64$

Step3: Calculate proper subsets

Proper subsets = $2^n - 1 = 64 - 1 = 63$

Answer:

(a) 63
(b) 64