Question

A set is given using set-builder notation as x is any integer/ 13/4 < x < 31/8. Explain why this set has no elements in it (known as an empty set). a) The range is outside the domain of integers b) There is a typographical error c) The inequality is contradictory d) The set-builder notation is incomplete

Answer 1

The given set is empty because the range 13/4 to 31/8 does not contain any integers, which is outside the domain of integers (whole numbers).

Step-by-step explanation:

The set defined as x is any integer is an empty set because the specified range does not include any integers. The inequality 13/4 < x < 31/8 translates to a range approximately between 3.25 and 3.875. Since integers are whole numbers and there are no whole numbers that fall within this range, it is impossible for any integer to satisfy the condition. Therefore, the correct answer is (a) The range is outside the domain of integers, which makes the set have no elements.