Integers And Absolute Values
Properties of substraction of Integers
1. Closure Property:-
Observe the following
1. 25-75=-50
2. \(% MathType!MTEF!2!1!+-
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% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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( - 125) - ( - 225) = - 125 + 225 = 100
\)
We observe that the difference of two Integers is always an Integer. So, we can say teh Integers are closed under substaraction.
Conclusion :- for any ‘2’ Integers (a-b) is also an Integer.
This property is called Closure Property for Integer over substarction.
2. Commutative Property :-
Observe the following
1. i) 75-25=50 ii) 25-75=-50
2. i) 200-100=100 ii) 100-200= -100
We deserve that the order of substraction changes the difference. Therefore we can communative property does not hold good over substaction.
conclusion of a and b are any two Integers, then a-b = b-a
3. Associative Property
Observe the following :
1. i)\(
6 - (3 - 2) = 5 - 1 = 4
\) ii)\(
(5 - 1) - 2 = 2 - 2 = 0
\)
2. i) \(
16 - (8 - 4) = 16 - 4 = 12
\) ii)\(
(16 - 8) - 4 = 8 - 4 = 4
\)
1st Integer = (2nd Integer-3rd Integer)\(
\ne
\)(1st Integer-2nd Integer)-3rd Integer
In this case associative law does not hold good over substraction
\(
\forall a,b,c \in
\)
we can say \(
a(b - c) \ne (a - b) - c
\)
if a.b and c are Integers and \(
a > b = c
\) a-c>b-c.