Q11 of 162 Page 1

What is the total number of proper subsets of a set consisting of n elements?

A total number of subsets for any given ser is 2ⁿ.

In every set there is only one improper set.

∴ proper subsets would be 2ⁿ–1.

Write down all possible subsets of each of the following sets:

Total number of the subset of any given set =2ⁿ

(i) {a}

(ii) {0,1}

(iii) {a,b,c}

(iv) {1,{1}}

(v) {ϕ}

Write down all possible proper subsets each of the following sets.

(i) {1,2}

(ii) {1,2,3}

(iii) {1}

If A is any set, prove that: A ϕ A=ϕ.

Prove that: A B, B C and C A A = C.