properties of equality and real numbers Flashcards
a=a
reflexive property
a=b —> b=a
symmetric property
(a = b /\ b = c) —> a=c
transitive property
a=b —> 3a + 1 = 3b + 1
substitution property
a=b —> a+c = b+c
addition property
a=b —> a-c = b-c
subtraction property
a=b —> a/c = b/c
multiplication property
a=b —> a/c = b/c
division property
a=b —> a2 = b2
exponent property
a=b —> -/a = -/b
square root property
a+b +c —> b+ a + c
commutative property of addition
a x b x c —> b x a x c
commutative property of multiplication
a+b (b+c) —> (a+b) + c
associative property of addition
a - (b+c) —> (a+b) + c
associative property of multiplication
a(b+c) —> ab + bc
distributive property
a+0 = a
identity property of addition
a-0 = a
identity property of subtraction
a x 1 = a
identity property of multiplication
a/1 = a
identity property of division
a+(-a) = 0
additive inverse property
a - (1/a) = 1
multiplicative inverse property