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PA Prop Ch1-3

NameSymbols
Substitution If a = b then a can be replaced by b
Commutative (Addition) a + b = b + a
Commutative (Multiplication) ab = ba
Associative (Addition) (a + b) + c = a + (b + c)
Associative (Multiplication) (ab)c = a(bc)
Identity (Addition) a + 0 = a
Identity (Multiplication) a x 1 = a
Zero Product a x 0 = 0
Symmetric If a = b then b = a
Transitive If a = b and b = c, then a = c
Inverse (Addition) a + (–a) = 0
Distributive a(b+c) = ab + ac
Addition Property of Equality if a = b then a + c = b + c
Multiplication Property of Equality if a = b then ac = bc
Inverse (Multiplication) a x 1/a = 1
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