Which of the following statements is/are true:

1. Subtraction on the set of all natural numbers is a binary operation.
2. Subtraction on the set of all integers is a binary operation

Concept:

An operation * on a non-empty set S, is said to be a binary operation if it satisfies the closure property.

Closure Property:

Let S be a non-empty set and a, b ∈ S, if a * b ∈ S for all a, b ∈ S then S is said to be closed with respect to operation *.

Calculation:

Statement 1: Subtraction on the set of all natural numbers is a binary operation.

Let a = 1, b = 2 ∈ N and here the operation is '-'

⇒ a - b = 1 - 2 = - 1 ∉ N

So, we can say that N is not closed with respect to the operation '-'

Hence, statement 1 is false.

Statement 2: Subtraction on the set of all integers is a binary operation.

Let a, b ∈ Z and here the operation is '-'

As we know that the resultant of subtraction of two integers is again an integer.

i.e a - b ∈ Z ∀ a, b ∈ Z.

So, Z is closed with respect to the operation '-'

Hence, statement 2 is true.

So, option B is correct answer.