###
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

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