Proving Statements

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1/12 Questions

There is a unique real number 0 such that for every real number a, a + 0 = a and 0 + a = a.
- Associate Axiom for addition
- Axiom of Opposites
- Identity Axiom for Addition

About This Quiz

Select the correct answer from the choices provided.

2.

For all real number a and b: a + b = b + a ab = ba
- Commutative Axioms
- Multiplicative Property of Zero
- Axioms of Reciprocals
Correct Answer

A. Commutative Axioms
3.

There is a unique real number 1 such that for every real number a, a 1 = a and 1 a = a.
- Identity Axiom for Multiplication
- Commutative Axioms
- Associative Axiom for Multiplication
Correct Answer

A. Identity Axiom for Multiplication
4.

For all real numbers a, b, and c: (a + b) + c = a + (b + c)
- Axiom of Closure
- Associative Axiom for Addition
- Distributive Axiom
Correct Answer

A. Associative Axiom for Addition
5.

For all real numbers, a, b, and c: If a = b and b =c, then a = c
- Axiom of Equality for Reflexive Property
- Axiom of Equality for Symmetric Property
- Axiom of Equality for Transitive Property
Correct Answer

A. Axiom of Equality for Transitive Property
6.

For every nonzero real number a, there is a unique real number such that: a = 1 and a = 1.
- Multiplicative Property of Zero
- Axiom of Reciprocals
- Property of the Reciprocal of a Product
Correct Answer

A. Axiom of Reciprocals
7.

For every real number a; there is a unique real number -a such that: a + (-a) = 0 and -a + a = 0
- Identity Axiom for Addition
- Opposite Axiom
- Commutative Axioms
Correct Answer

A. Opposite Axiom
8.

Select the missing reason from the choices below.
- Identity axiom for multiplication
- Rule for subtraction
- Subtraction property of equality
Correct Answer

A. Subtraction property of equality
9.

If a, b, and c are any real numbers and a = b, then: a + c = b + c and c + a = c + b.
- Addition Property of Equality
- Identity Axiom of Addition
- Associative Axiom for Addition
Correct Answer

A. Addition Property of Equality
10.

For all real numbers, a, b, and c: If a = b, then b = a.
- Axiom of Equality for Reflexive Property
- Axiom of Equality for Symmetric Property
- Axiom of Equality for Transitive Property
Correct Answer

A. Axiom of Equality for Symmetric Property
11.

For every real number a, a (-1) = -a and (-1) a = -a.
- Multiplicative Property of Zero
- Identity Axiom for Multiplication
- Multiplicative Property of -1
Correct Answer

A. Multiplicative Property of -1
12.

Select the missing reason from the choices below.
- Property of the reciprocal of a product
- Commutative axiom
- Axiom of reciprocals
Correct Answer

A. Axiom of reciprocals

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Jul 09, 2017

Quiz Edited by
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Jun 22, 2012

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Proving Statements

There is a unique real number 0 such that for every real number a, a + 0 = a and 0 + a = a.

Quiz Preview

For all real number a and b: a + b = b + a ab = ba

There is a unique real number 1 such that for every real number a, a 1 = a and 1 a = a.

For all real numbers a, b, and c: (a + b) + c = a + (b + c)

For all real numbers, a, b, and c: If a = b and b =c, then a = c

For every nonzero real number a, there is a unique real number such that: a = 1 and a = 1.

For every real number a; there is a unique real number -a such that: a + (-a) = 0 and -a + a = 0

Select the missing reason from the choices below.

If a, b, and c are any real numbers and a = b, then: a + c = b + c and c + a = c + b.

For all real numbers, a, b, and c: If a = b, then b = a.

For every real number a, a (-1) = -a and (-1) a = -a.

Select the missing reason from the choices below.