Exam (elaborations)
AXIOM STRUCTURE QUESTIONS AND ANSWERS
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AXIOM STRUCTURE QUESTIONS AND ANSWERS
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Name: Score:20 Multiple choice questions
Definition 1 of 20
3 + (-3) = 0
x + (-x) = 0
Example 4: Additive Inverse Property
Example 20: Additive Inverse Property
Example 4: Multiplicative Inverse Property
Example 0: Additive Inverse Property
Definition 2 of 20
3∙1=3
x∙1=x
Example 3: Identity Property
Example 6: Zero Property
Example 4: Additive Inverse Property
Example 1: Commutative Property
Definition 3 of 20
commutative - addition
distributive
Choose 2 axioms that indicate 22 + (m + 8) is equivalent to 22m.
Choose 2 axioms that state 22 + (m + 8) must equal 30 + m.
Choose 2 axioms that allows 22 + (m + 8) to be written as m + 30
Choose 2 axioms that allow the addition of m and 8 to be separated from 22.
,Definition 4 of 20
3 + (5 + 2) = (3 + 5) + 2
4 + (2 + x) = (4 + 2) + x
(x + 4) + (y + 3) = (x + 4 + y) + 3
Example 3: Identity Property
Example 1: Commutative Property
Example 5: Distributive Property
Example 2: Associative Property
Definition 5 of 20
6∙0=0
x∙0=0
(a - b) 0 = 0
Example 3: Identity Property
Example 1: Commutative Property
Example 6: Zero Property
Example 4: Multiplicative Inverse Property
Definition 6 of 20
5∙=1
AB ∙ = 1; AB 0
x ∙ = 1; x 0
Example 4: Multiplicative Inverse Property
Example 8: Multiplicative Inverse Property
Example 2: Multiplicative Inverse Property
Example 5: Multiplicative Inverse Property
, Definition 7 of 20
A. commutative a + b = b + a
B. associative a + (b + c) = (a + b) + c
C. identity a + 0 = a
D. additive inverse a + (-a) = 0
PROPERTIES OF MULTIPLICATION
More Properties
PROPERTIES OF ADDITION
1. 8 = 8
2. If x = y, then y = x
3. If x = y and y = 7, then x = 7
4. 6 + 2 = 2 + 6
5. 5 ∙ 2 = 2 ∙ 5
6. 10 + (3 + 2) = (10 + 3) + 2
7. 6(3 ∙ 5) = (6 ∙ 3)5
8. 4(8 + 1) = 4 ∙ 8 + 4 ∙ 1
9. 6 + 0 = 6
10. 8 ∙ 1 = 8
11. 2 = 1
12. 5 ∙ 0 = 0
Definition 8 of 20
2+3=3+2
2+x=x+2
x + (3 + y) = (3 + y) + x
Example 3: Identity Property
Example 2: Associative Property
Example 1: Commutative Property
Example 6: Zero Property
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