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# Algerbre 2 propertie

### Pg. 14 - 15

Reflexive Property a = a
Symmetric Property If a=b, then b=a.
Transitive Property If a=b and b=c, the c=a.
Addition Property If a=b, then a+c=b+c and c+a=c+b.
Multipication Property If a=b, then ac=bc and ca=cb.
Closure Properties a+b and ab are unique real numbers.The sum of 12 and 6 is the real number 18; the product of 12 and 6 is the real number 72.
Commutative Properties a+b=b+a ab=ba. 12+6=6+12 12*6=6*12.
Associative Properties (a+b)+c=a+(b+c) (ab)c=a(bc). (12+6)+5=12+(6+5) (12*6)*5=12*(6*5)
Identity Properties There are unique real numbers 0 and 1 (1=/0) such that: a+0=a and 0+a=a a*1=a and 1*a=a and 12+0=12 and 0+12=12 12*1=12 and 1*12=12.
Inverse Properties 1/a*a=1. (1/a is called the reciprocal or multiplicative inverse of a. Property of opposites:For each a, there is a unique real number -a such that:a+(-a)=0 and (-a)+a=0.(-a is called the opposite or additive inverse of a.) Property of Reciprocals:For each a except 0, there is a unique real number 1/a such that:a*1/a=1 and
Distriputive property (of multipication with respect to addition) a(b+c)=ab+ac and (b+c)a=ba+ca
Created by: Dudlee13