Question

State, whether the following pairs of sets are equivalent or not : 

(i) A = {x : x ∈ N and 11 ≥ 2x – 1} and B = {y : y ∈ W and 3 ≤ y ≤ 9} 

(ii) Set of integers and set of natural numbers. 

(iii) Set of whole numbers and set of multiples of 3. 

(iv) P = {5, 6, 7, 8} and M = {x : x ∈ W and x < 4} 

Note : Two sets are said to be equivalent, if they contain the same number of elements.

Answer 1

B = {3,4,5,6,7,8,9} 

n (B) = 7 

Cardinal number of set A = 6 and cardinal number of set B = 7 

Set A and set B are not equivalent.

(ii) Set of integers has infinite number of elements. Set of natural numbers has infinite number of elements. 

Set of integers and set of natural numbers are equivalent because both these sets have infinite number of elements.

(iii) Set of whole numbers, has infinite number of elements. Set of multiples of 3, has infinite number of element. 

Set of whole numbers and set of multiples of 3 are equivalent because both these sets have infinite number of elements.

(iv) P = {5,6,7,8} 

n (P) = 4 

M = {x : x ∈ W and x ≤ 4} 

M = {0, 1, 2, 3, 4} 

n (M) = 5 Now Cardinal number of set P = 4 and 

Cardinal number of set M = 5 

These sets are not equivalent.