
{1,2,3,..........} is called the set of Natural Numbers and is denoted by 'N'.
Properties of Natural Numbers in Addition
Closure Property: For any two natural numbers "a" and "b" their sum (a+b) is also a natural number. This is called the closure property of addition for natural numbers.
Commutative Property: For any two natural numbers "a" and "b"
a+b = b+a. This property is called commutative property of addition for natural numbers.
Associative Property: For any three natural numbers a, b, and c,
a+(b+c) = (a+b)+c. This property is called the associative property of addition for natural number.
Example: 3, 5 and 7 are three natural numbers, Then 3 + (5 + 7) = (3 + 5) + 7
3 + (5 + 7) = 3 + 12 = 15
Properties of Natural Numbers in Multiplication
Closure Property: For any two natural numbers a and b
their product a*b is also a natural number. This property is called the closure property of multiplication for natural number.
Example: 3, 5 are natural numbers, Then 3 x 5 is also a natural number
Commutative Property: For any two natural numbers a and b
a*b =b*a. This is called the commutative property of multiplication in natural numbers.
Example: 3, 5 are natural numbers, Then 3 x 5 = 5 x 3
Associative Property: For any three natural numbers a, b, and c
a*(b*c) = (a*b)*c. This is called the associative property of multiplication in natural numbers.
Example: 2, 3 and 4 are natural numbers, Then 2 x (3 x 4) = (2 x 3) x 4
Multiplicative Identity: For any natural number a,
a*1 = 1*a = a. Here 1 is called the multiplicative identity in the set of all natural numbers. Directions: Answer the following questions. Write these properties and prove that they do not hold true for for subtraction and division. Also, write at least five examples of each property. 