Relations And Functions

• Question

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

Solution

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