Write down all the subsets of the following sets (i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ

Solution:

We say that a set A is a subset of a set B if all the elements of A are also present in B.

Note that Φ represents an empty set (a set without any elements) and hence it is a subset of every set.

Thus,

(i) The subsets of {a} are Φ and {a}.

(ii) The subsets of {a, b} are Φ, {a}, {b} and {a, b} .

(iii) The subsets of {1, 2, 3} are Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} and {1, 2, 3}

(iv) The only subset of Φ is Φ.

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.3 Question 4

Write down all the subsets of the following sets (i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ

Summary:

We found that 
(i) The subsets of {a} are Φ and {a} 
(ii) The subsets of {a, b} are Φ, {a}, {b} and {a, b} 
(iii) The subsets of {1, 2, 3} are Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} and {1, 2, 3}
(iv) The only subset of Φ is Φ