Exam (elaborations)
AXIOMS TEST QUESTIONS AND ANSWERS
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AXIOMS TEST QUESTIONS AND ANSWERS
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Name: Score:37 Multiple choice questions
Term 1 of 37
INVERSE NOTE 1
(1/a) is called the multiplicative inverse of a or the reciprocal of a
1 is called the multiplicative identity element
(-a) is called the additive inverse of a
0 is called the additive identity element
Term 2 of 37
What is the inverse axiom for addition?
A(1) = 1(a) = a, where 1 is unique
A + (b + c) = (a + b) + c
A(1/a) = (1/a)a = 1 where 1/a is unique, a ≠ 0
A + (-a) = (-a) + a = 0 where -a is unique
Term 3 of 37
What is the abbreviation for reflexive axiom of equality?
SYM
ADD
REF
TRANS
,Term 4 of 37
What is the Addition property of equality?
If a = b and c = d, then ac = bd
If a = b and b = c, then a = c
If a = b and c = d, then a + c = b + d
If a, b, and c are real numbers, then the following axioms are true
Term 5 of 37
What is the commutative axiom for addition?
A + (b + c) = (a + b) + c
A - b = a + (-b)
A(b+c) = ab + ac
A+ b= b+a
Term 6 of 37
What is the Reflexive axiom of equality?
A+ b= b+a
Ab=ba
A - b = a + (-b)
a=a
Term 7 of 37
What are the identity axioms?
INV-A and INV-M (inverse axiom for addition, inverse axiom for multiplication)
C-A and C-M (commutative axiom for addition and commutative axiom for multiplication)
ID-A and ID-M (identity axiom for addition, identity axiom for multiplication)
CLO-A and CLO-M (closure axiom of addition, closure axiom of multiplication)
,Term 8 of 37
What is the definition of division?
If a = b then b = a
A/b = a(1/b) , b ≠ 0
A + (b + c) = (a + b) + c
A(1) = 1(a) = a, where 1 is unique
Term 9 of 37
What is form one of the distributive axiom?
(A+b)c = ac + bc
A(b+c) = ab + ac
A+ b= b+a
A - b = a + (-b)
Term 10 of 37
What is the identity axiom for multiplication?
If a = b and c = d, then ac = bd
A(1) = 1(a) = a, where 1 is unique
A + 0 = 0 + A = A, where 0 is unique
A(1/a) = (1/a)a = 1 where 1/a is unique, a ≠ 0
Term 11 of 37
What is the commutative axiom for multiplication?
a=a
A+ b= b+a
TRANS
Ab=ba
, Term 12 of 37
IDENTITY NOTE 2
A + (-a) = (-a) + a = 0 where -a is unique
0 is called the additive identity element
(1/a) is called the multiplicative inverse of a or the reciprocal of a
1 is called the multiplicative identity element
Term 13 of 37
What is the multiplication property of Equality?
If a, b, and c are real numbers, then the following axioms are true
A(1) = 1(a) = a, where 1 is unique
If a = b and c = d, then ac = bd
If a = b and c = d, then a + c = b + d
Term 14 of 37
What is the Distribute axiom abbreviation?
a=a
A + (b + c) = (a + b) + c
ADD
D
Term 15 of 37
What is the closure axiom of multiplication?
A + 0 = 0 + A = A, where 0 is unique
Ab=c, where c is a unique real number
A+b=c, where C is a unique real number
If a = b and c = d, then a + c = b + d
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