Basic Law of Natural Numbers
Let a, b and c be any number.
1. Law of closure for addition:
a + b
2. Commutative law for addition:
a + b = b + a
EXAMPLE 1:
2 + 3 = 3 + 2
5 = 5
3. Associative law for addition:
a + ( b + c ) = (a + b ) + c
EXAMPLE 1:
5 + ( 2 + 7 ) = (5 + 2 ) + 7
14 = 14
4. Law of closure for multiplication:
a * b
5. Commutative law for multiplication:
a * b = b * a
EXAMPLE 1:
3 * 4 = 4 * 3
12 = 12
6. Associative law for multiplication:
a ( bc ) = ( ab ) c
EXAMPLE 1:
3 [( 2 )( 5 )] = [( 3 )( 2 )] 5
30 = 30
7. Distributive law:
a ( b + c ) = a b + ac
EXAMPLE 1:
2 ( 4 + 7 ) = ( 2 )( 4 ) + ( 2 )( 7 )
22 = 22
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