The set of real numbers R comprises all numbers on the continuous number line, consisting of both rational numbers and irrational numbers. The set Q contains all rational numbers, which can be expressed as a ratio of 2 integers with a non-zero denominator.

The set of real numbers R comprises all numbers on the continuous number line, consisting of both rational numbers and irrational numbers. The set Q contains all rational numbers, which can be expressed as a ratio of 2 integers with a non-zero denominator.

By definition, the set difference A - B represents all elements that belong to set A but do not belong to set B. Therefore, R - Q is the collection of all real numbers that are not rational numbers.

Any real number that cannot be expressed as a quotient of 2 integers is defined as an irrational number (often denoted by T or I). Examples include √2, √3, and π. Hence, removing all rational numbers from the real numbers leaves precisely the set of irrational numbers.

Any real number that cannot be expressed as a quotient of 2 integers is defined as an irrational number (often denoted by T or I). Examples include √2, √3, and π. Hence, removing all rational numbers from the real numbers leaves precisely the set of irrational numbers.

Id R is the set of real numbers and Q is the set of rational question then what is R-Q?

Answer: The set of irrational numbers

Step-by-step solution

Step 1: Define the universal set and subset

The set of real numbers $\mathbb{R}$ comprises all numbers on the continuous number line, consisting of both rational numbers and irrational numbers. The set $\mathbb{Q}$ contains all rational numbers, which can be expressed as a ratio of 2 integers with a non-zero denominator.

Step 2: Apply the definition of set difference

By definition, the set difference $A - B$ represents all elements that belong to set $A$ but do not belong to set $B$ . Therefore, $\mathbb{R} - \mathbb{Q}$ is the collection of all real numbers that are not rational numbers.

Step 3: Identify the resulting set

Any real number that cannot be expressed as a quotient of 2 integers is defined as an irrational number (often denoted by $\mathbb{T}$ or $\mathbb{I}$ ). Examples include $\sqrt{2}$ , $\sqrt{3}$ , and $\pi$ . Hence, removing all rational numbers from the real numbers leaves precisely the set of irrational numbers.

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