Axioms - M413 Exam 1 Questions and Answers 100% Correct

Axioms - M413 Exam 1 Questions
and Answers 100% Correct
A1 - ANSWER - a + (b + c) = (a + b) + c (associativity)


M1 - ANSWER - a(bc) = (ab)c (associativity)


A2 - ANSWER - a + b = b + a (commutativity)


M2 - ANSWER - ab = ba (commutatitivty)


A3 - ANSWER - there is an element 0 that belongs to F such that a + 0 = a
(identities)


M3 - ANSWER - there is an element 1 that belongs to F such 1*a = a (identities)


A4 - ANSWER - for every a, there is b in F such that a + b = 0, call b the additive
inverse of a and write -a for b (inverses)


M4 - ANSWER - for every a, there is b in F such that ab = 1, call be the multiplicative
inverse of a, write a^-1 for b


DL - ANSWER - a(b + c) = ab + ac (distributivity)


O1 - ANSWER - either a ≤ b or b ≤ a


O2 - ANSWER - if a ≤ b and b ≤ a, then a = b


O3 - ANSWER - if a ≤ b and b ≤ c, then a ≤ c (transitivity)