1)    a)  From the set {-5, 3+4i, 0.25, 6, ½ , √(-49), √2, 3i,  -1/5, 8, √7} i) List the set of           Natural Numbers ii) List the set of          Rational Numbers iii) List the set of         Irrational Numbers vi) List the set of         Real Numbers                                                              b) Calculate             i)  6 x (-4) - (-17 + 8)  + 6 x (-3) =      ii)  -6(-4) - 3(-5) + 3(-3)  =                                                                                  5(-4)+ (-2)7 - 8(-4)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 13E: 13. Prove that if and are rational numbers such that then there exists a rational number such...
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1)    a)  From the set {-5, 3+4i, 0.25, 6, ½ , √(-49), √2, 3i,  -1/5, 8, √7}

i) List the set of           Natural Numbers

ii) List the set of          Rational Numbers

iii) List the set of         Irrational Numbers

vi) List the set of         Real Numbers                                                           

 

b) Calculate

            i)  6 x (-4) - (-17 + 8)  + 6 x (-3) =      ii)  -6(-4) - 3(-5) + 3(-3)  =

                                                                                 5(-4)+ (-2)7 - 8(-4)                      

Expert Solution
Step 1

I)

Natural numbers include all the whole numbers excluding the number 0

{6}

II)

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero

{-5, 0.25, 6, ½ , -1/5, 8}

III)

an irrational number cannot be expressed in the form of fractions

{√2,√7}

IV)

Real numbers are the numbers that include both rational and irrational numbers. 

{-5, 0.25, 6, ½ , , √2,  -1/5, 8, √7}

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