Question

Set of natural numbers A = $\{x:x\in N\}$ is a proper subset of which of the following

• A. Set of whole numbers $A_1=\{x:xϵW\}$
• B. Set of Real numbers $A_2=\{x:xϵR\}$
• C. Set of Integers $A_3=\{x:xϵI\}$
• D. All of the above.

Answer 1

The correct option is D All of the above.

Set A is said to be a proper subset of B if A is a subset of B and A $\ne$ B i.e if
(i) Every element of A is an element of B
(ii) B has atleast one element which is not an element of A.

All natural numbers belong to the set of whole numbers but 0 does not belong to the set of natural numbers. Hence, set of natural numbers is a proper subset of set of whole numbers.

All natural numbers belong to the set of integers but negative integers do not belong to the set of natural numbers. Hence, set of natural numbers is a proper subset of set of integers.

All natural numbers belong to the set of real numbers but rational numbers do not belong to the set of natural numbers. Hence, set of natural numbers is a proper subset of set of real numbers.