Proving Statements

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

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Proving Statements - Quiz

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

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3. There is a unique real number 1 such that for every real number a,  a «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#183;«/mo»«/math» 1 = a   and   1 «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#183;«/mo»«/math» a = a.   

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

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

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6. For every nonzero real number a, there is a unique real number «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mi»a«/mi»«/mfrac»«/math» such that: a «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#183;«/mo»«/math»«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mi»a«/mi»«/mfrac»«/math» = 1 and «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mi»a«/mi»«/mfrac»«/math» «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mo»§#183;«/mo»«/math» a = 1. 

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7. Select the missing reason from the choices below. 

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

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

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

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

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12. Select the missing reason from the choices below.

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There is a unique real number 0 such that for every real number...
For all real number a and b:...
There is a unique real number 1 such that for every real number...
For all real numbers a, b, and c: ...
For all real numbers, a, b, and c: ...
For every nonzero real number a, there is a unique real...
Select the missing reason from the choices below. 
For every real number a; there is a unique real number -a such that:...
If a, b, and c are any real numbers and a = b, then:...
For all real numbers, a, b, and c: ...
For every real number a, a (-1) = -a and (-1) a = -a.
Select the missing reason from the choices below.
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