Complete the following table:
|
Numbers |
Associative for |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
No |
|||
|
Integers |
Yes |
|||
|
Whole numbers |
Yes |
|||
|
Natural numbers |
No |
|||
|
Numbers |
Associative for |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
Yes |
No |
Yes |
No |
|
Integers |
Yes |
No |
Yes |
No |
|
Whole numbers |
Yes |
No |
Yes |
No |
|
Natural numbers |
Yes |
No |
Yes |
No |
Complete the following table:
|
Numbers |
Commutative for |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
Yes |
... |
||
|
Integers |
No |
|||
|
Whole numbers |
Yes |
|||
|
Natural numbers |
No |
|||
|
Numbers |
Commutative for |
||||
|
Addition |
Subtraction |
Multiplication |
Division |
||
|
Rational numbers |
Yes |
No |
Yes |
No |
|
|
Integers |
Yes |
No |
Yes |
No |
|
|
Whole numbers |
Yes |
No |
Yes |
No |
|
|
Natural numbers |
Yes |
No |
Yes |
No |
|
Complete the following table:
|
Numbers |
Commutative for |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
Yes |
... |
||
|
Integers |
No |
|||
|
Whole numbers |
Yes |
|||
|
Natural numbers |
No |
|||
|
Numbers |
Commutative for |
||||
|
Addition |
Subtraction |
Multiplication |
Division |
||
|
Rational numbers |
Yes |
No |
Yes |
No |
|
|
Integers |
Yes |
No |
Yes |
No |
|
|
Whole numbers |
Yes |
No |
Yes |
No |
|
|
Natural numbers |
Yes |
No |
Yes |
No |
|
Complete the following table:
|
Numbers |
Associative for |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
No |
|||
|
Integers |
Yes |
|||
|
Whole numbers |
Yes |
|||
|
Natural numbers |
No |
|||
|
Numbers |
Associative for |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
Yes |
No |
Yes |
No |
|
Integers |
Yes |
No |
Yes |
No |
|
Whole numbers |
Yes |
No |
Yes |
No |
|
Natural numbers |
Yes |
No |
Yes |
No |
Fill in the blanks in the following table:
|
Numbers |
Closed under |
|||
|
Addition |
Subtraction |
Multiplication |
Division |
|
|
Rational numbers |
Yes |
Yes |
No |
|
|
Integers |
Yes |
No |
||
|
Whole numbers |
... |
Yes |
||
|
Natural numbers |
No |
|||
Using the closure property over addition, subtraction, multiplication and division for rational numbers, integers, whole-numbers and natural numbers, we have:
|
Numbers |
Closed under |
||||
|
Addition |
Subtraction |
Multiplication |
Division |
||
|
Rational numbers |
Yes |
Yes |
Yes |
No |
|
|
Integers |
Yes |
Yes |
Yes |
No |
|
|
Whole numbers |
Yes |
No |
Yes |
No |
|
|
Natural numbers |
Yes |
No |
Yes |
No |
|
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