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QuestionFind the set of numbers that are both rational and irrational. Choose the correct set: A. ∅\varnothing B. {0}\{0\} C. {x,−x}\{\sqrt{x}, \sqrt{-x}\} D. {0,1,2,3,4,5,…}\{0,1,2,3,4,5, \ldots\}

Studdy Solution

STEP 1

Assumptions1. A rational number can be expressed as a ratio of two integers, where the denominator is not zero. . An irrational number cannot be expressed as a ratio of two integers.
3. We are looking for the set of numbers that are both rational and irrational.

STEP 2

By definition, a number cannot be both rational and irrational at the same time. This is because the definitions of rational and irrational numbers are mutually exclusive.

STEP 3

Therefore, the set of numbers that are both rational and irrational is the empty set.
{x∣x is a number that is both rational and irrational}=∅\{x \mid x \text{ is a number that is both rational and irrational} \} = \varnothingSo, the correct answer is A. ∅\varnothing.

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