Problem 90 - College Algebra

Question

Which one of the following statements is true? a. Every rational number is an integer. b. Some whole numbers are not integers. c. Some rational numbers are not positive. d. Irrational numbers cannot be negative.

Step-by-Step Solution

Answer

c. some rational numbers are not positive.

Step 1: Understanding the terms

Rational numbers are all the numbers that can be written as a fraction. Integers are all whole numbers both positive and negative, including zero. Whole numbers are all positive integers including zero. Irrational numbers are any real numbers that are not rational, meaning they can't be represented as a quotient of two integers.

Step 2: Evaluate statement a

'Every rational number is an integer' is false. Rational numbers include fractions and integers, not just integers.

Step 3: Evaluate statement b

'Some whole numbers are not integers' is false. By definition, all whole numbers are integers.

Step 4: Evaluate statement c

'Some rational numbers are not positive.' is true. Rational numbers include both positive and negative numbers, as well as zero.

Step 5: Evaluate statement d

'Irrational numbers cannot be negative.' is false. Irrational numbers can be both positive and negative.