Question

LET'S PRACTICE 1.4
1. State which of the following statements are true or false ? Also, justify by giving an example.
(i) The collection of integers obey closure property for division.
(ii) The collection of integers is commutative under multiplication.
(iii) The collection of integers is commutative under division.
(iv) The distributive property of '÷' over '+' holds good in case of integers.
(v) Division by 1 is undefined.
(vi) Division of any integer by O always gives 0.
SIG QUR NUMBERS​

Answer 1

Answer:

Integers are commutative under addition when any two integers are added irrespective of their order, the sum remains the same.

a+b =b+a

The sum of two integer numbers is always the same. This means that integer numbers follow the commutative property.

Let’s see the following examples:

15 + 20 =35; 20 +15=35

-10 + (-5) = -15; -5 + (-10) = -15

The above examples prove that the addition of integers is commutative.

The commutative property for Subtraction:

Is the case true with subtractions? Are subtractions also commutative? The following examples will let us know this:

5-(-3) = +8

-3-5 = -8

This brings us to the conclusion that subtractions of integers are not commutative. Therefore, a-b ≠ b-a

Commutative Property of Division

This property does not apply to divisions between integers. This means that a÷b ≠b÷a

Option A is correct