Relations and Functions

Relations and Functions

Question

Write down all the subsets of the following sets

(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ

Answer


(a) A   =  {a}

Number of elements in set A = 1
rightwards double arrow  Number of subsets = 2= 2

∴ The subsets are  φ, {a}

(b)      A   =  {a, b}
Number of elements in set A = 2

rightwards double arrow  Number of subsets = 2= 4

 

∴ The subsets are  φ, {a}, {b}, {a, b}

(c)  A   =  {1, 2, 3}
Number of elements in set A = 3

rightwards double arrow Number of subsets = 2= 8

∴ The subsets are  φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} and {1, 2, 3}

(d)   φ  = {  }
Number of elements  = 0
rightwards double arrow  Number of subsets = 2= 1
∴ The subsets is φ

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