4 Indicate whether each statement is false or true. If false, explain:
a Between any two rational numbers, there is always a rational number
b The set of real numbers is the union of the set of rational numbers and the
set of irrational numbers.
The set of rational numbers is closed under addition, subtraction,
multiplication and division excluding division by zero.
d
The set of irrational numbers is closed under addition, subtraction,
multiplication and division.
Give examples to show each of the following:
a The product of two irrational numbers may be rational or irrational.
b The sum of two irrational numbers may be rational or irrational.
The difference of two irrational numbers may be rational or irrational.
d The quotient of two irrational numbers may be rational or irrational,
Demonstrate with an example that the sum of an irrational number and a rational
number is irrational.
Demonstrate with an example that the product of an irrational number and a non-
zero rational number is irrational.
5