which statement is true?

Question

A. every real number is an integer
B. every integer is a counting number
C. every integer is a rational number
D. every terminating decimal number is an irrational number

Answer 1

The true statement among the options provided is:

C. every integer is a rational number.

Explanation:

• A. Every real number is an integer: This is false because real numbers include rational and irrational numbers, whereas integers are a specific subset of real numbers.
• B. Every integer is a counting number: This is false because integers include negative numbers (e.g., -1, -2) which are not counting numbers (counting numbers start from 1 and include only positive whole numbers).
• C. Every integer is a rational number: This is true because any integer can be expressed as a fraction (e.g., \( n = \frac{n}{1} \)), which fits the definition of rational numbers.
• D. Every terminating decimal number is an irrational number: This is false because terminating decimal numbers (like 0.5 or 1.25) are rational numbers, not irrational.

Thus, the correct option is C.