Introduction to Proving

 

One of the many ways to be more accustomed or familiar with Proving, we can start by reviewing the different properties involved with it.

Such as:

Properties of Real Numbers

Closure Property
-If a and b are real numbers then (a+b) or (a-b) are real numbers.


Commutative Property
- a+b=b+a
     ab=b+a


Associative Property
-  a+(b+c) - (a+b) c


Distributive Property
- a( b+c) = ab+ac


Additive Propert
- a+0 = a


Multiplicative Property
- a(1) = a



Inverse Property
-a+(a)=0  a(1/a)= 1

Properties of Equality

Reflexive Property
- a=a


Symmetric Property
- a=b, b=a


Transitive property
- If a=b ; & b=c then a=c

Properties of Congruence

Reflexive Property
-


Symmetric Property
-


Transitive Property
-