Question

let the set a be defined as follows. a = {74, 71, 45, 28, 23, 18, 1} (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

Count of elements $n = 7$

Step2: Calculate total subsets

Total subsets = $2^n = 2^7 = 128$

Step3: Calculate proper subsets

Proper subsets = $2^n - 1 = 128 - 1 = 127$

Answer:

(a) 127
(b) 128