A real number may be either rational or irrational; either algebraic or transcendental; and either positive, negative, or zero. Real numbers are used to measure continuous quantities.

Explanation:

To understand why the correct answer is option 'D', let's first define what it means for a number to be rational or irrational.

1. Rational Numbers:
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number can be written in the form p/q, where p and q are integers and q is not equal to zero.

Examples of rational numbers include 1/2, -3/4, 5, -7, etc.

2. Irrational Numbers:
An irrational number is any number that cannot be expressed as a fraction or quotient of two integers. These numbers cannot be written as terminating or repeating decimals.

Examples of irrational numbers include π (pi), √2 (square root of 2), √3, etc.

Now, let's consider the statement "Every real number is either rational or irrational."

Proof:

1. Every Rational Number is Real:
It is a known fact that every rational number is a real number. This means that any number that can be expressed as a fraction of two integers is also a real number.

2. Every Irrational Number is Real:
Similarly, every irrational number is also a real number. Any number that cannot be expressed as a fraction or quotient of two integers is still considered a real number.

3. Every Real Number is Either Rational or Irrational:
Since every real number is either rational or irrational, we can conclude that every real number falls into one of these two categories. There are no real numbers that are neither rational nor irrational.

Therefore, the correct answer is option 'D' - every real number is either rational or irrational.

The combination of the rational and irrational numbers is known as the real numbers