Determine whether the statement is true or false.
-The intersection of the set of rational numbers with the set of irrational numbers is the empty set.

Question

Quizplus · Accepted Answer

A rational number is any number that can be expressed as a ratio of two integers, while an irrational number cannot be expressed as such. Therefore, the intersection of these sets is empty because there are no numbers that are both rational and irrational. This is true because by definition, a rational number is a number that can be expressed as the quotient or fraction p/q, where p and q are integers and q is not equal to 0. An irrational number, on the other hand, is a number that cannot be expressed as such a fraction. Therefore, there is no number that can belong to both sets at the same time, making their intersection empty.

Determine Whether the Statement Is True or False