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21 terms

Algebra II Properties

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reflexive
a=a
symmetric
if a=b, then b=a
transitive
if a=b, and b=c, then a=c
addition of equality
if a=b then a+c=b+c
multiplication of equality
if a=b then ac=bc
substitution
if a=b and a+c= then b+c=d
definition of subtraction
a-b=a+(-b)
definition of division
a/b=a*(1/b)
multiplication property of -1
(-1)*a=-a
multiplication property of 0
a*0=0
commutative (+)
a+b=b+a
commutative (*)
ab=ba
associative (+)
(a+b)+c=a+(b+c)
associative (*)
(ab)c=a(bc)
distributive
a(b+c)=ab+ac
additive identity
a+0=a
multiplicative identity
a*1=a
additive inverse
a+(-a)=0
multiplicative inverse
a*(1/a)=1
closure (+)
a+b has answer in set
closure (x)
ab has answer in set