Transitive Property Summary
Before going to summary of transitive property we need to know what is the meaning of transitive
. The word Transitive means relating to a relationship between three elements such that if the relationship holds between the first and second elements and between the second and third elements, it necessarily holds between the first and third elements.
In this summary of transitive property we are going to learn about
Transitive property of equality.
Transitive property of inequality.
Transitive property of congruence.
Related examples.
Summary of Transitive Property of Equality:
Consider that there are three numbers a,b,c .if a is equal to b and b is equal to c then it can be said that a is equal to c. This can be written as a=b and b=c then a=c.
This can be easily proved.
First given condition is a=b and b=c.
Now plug the value of b=c in a=b.
Then we get a=c. Hence proved.
Summary of Transitive Property of Inequality:
The transitive property of inequality is similar to that of transitive property of equality. The logic is illustrated as follows. consider there are three numbers a,b,c then if a is greater than b and b is greater than c then a is greater than c. This can be written as ab and bc then ac. There are large number of possible variations when applying transitive property of inequality. There are many possibilities that can be shown.
Consider that a,b,c are real numbers then
If ab and bc then ac
If ab and bc then ac
If a=b and b=c then a=c
If a=b and b=c then a= c
If a=b and bc then a c
If ab and b=c then a c
If ab and b=c then ac
If a=b and bc then ac
Summary of Transitive Property of Congruence.
Transitive property of congruence is related to geometry. This property is same as property of equality but here a,b,c are angles and if angle a= angle b and angle b= angle c then angle a = angle c.
Examples in Summary of Transitive Property
If 65 and 54 then 64
If 56 and 67 then 57
If 2=1 and 1=0 then 2=0
If 2=2 and 2=3 then 2=3
If 10=9 and 98 then 108
If 23 and 3=4 then 2 4
If 76 and 6=4 then 74
If 3=4 and 45 then 35
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This is about summary of transitive property .
Additive identity is one of the important concepts in elementary mathematics. Additive identity property involves the operation of addition of set of element.
Sum of zero with other number will yield the same number : this property is called Additive identity property. In this operation of addition the number zero is called additive identity.
For example, Element x is add with zero will yield x then this is called additive identity property. In group and ring the property of additive identity is applicable.
Here marhematically,
' 0+x=x+0=x'
Definition of Additive identity property:
Operation of addition performed with the set a and zero then the yield is a.
Example of Additive identity property:
The number 9 has to be adding with zero then according to the additive identity property the yield will be the number itself.
'9+0=0+9=9'
Problem 1:
In the below mentioned five expressions, which of the following satisfies the properties of additive identity properties.
Options: A) 8 + 0 = 8
B) -6 + 0 = 0
C) 7 0 = 0
D) 5 - 4 = 1
Solution :
Here option A i.e,8+0=8 satisfied the properties of additive identity. Adding 8 with 0 give us the yield of 8 so it satisfies the properties of additive identity.
Problem2:
Using additive identity property ,complete the below mentioned equation.
Option:
5+0=?
0+4=?
Solution: Additive identity property states that the addition of any element with zero will yield the same element.
So according to the properties- 5+0=5 and
0+4=4
Exercise for Additive identity property:
Problem1:
In the below mentioned five expressions, which of the following satisfies the properties of additive identity properties.
Options: A) 9 + 0 = 9
B) -7 + 0 = 0
C) 7 0 = 0
D) 6 - 5 = 1
[Solution:A]
Problem2:
Using additive identity property ,complete the below mentioned equation.
Option:
a)9+0=?
b)0+a=?
[Solution: a) 9, b) a]
by: mathqa
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