Math  /  Numbers & Operations

QuestionQ : All of the statements below are true except? A. Coprime numbers are numbers whose GCF is 1 B. A perfect number is a positive integer equal to the sum of its properties C. A complex number is a combination of a real number and an imaginary number D. All whole numbers are positive integers

Studdy Solution

STEP 1

1. We need to determine which statement among A, B, C, and D is false.
2. We will evaluate the truth of each statement individually to identify the incorrect one.

STEP 2

1. Evaluate the truth of statement A.
2. Evaluate the truth of statement B.
3. Evaluate the truth of statement C.
4. Evaluate the truth of statement D.
5. Identify the false statement.

STEP 3

Evaluate statement A: "Coprime numbers are numbers whose GCF is 1."
Statement A is true. By definition, two numbers are coprime (or relatively prime) if their greatest common factor (GCF) is 1.

STEP 4

Evaluate statement B: "A perfect number is a positive integer equal to the sum of its properties."
Statement B is false. The correct definition of a perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). For example, 6 is a perfect number because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.

STEP 5

Evaluate statement C: "A complex number is a combination of a real number and an imaginary number."
Statement C is true. A complex number is typically written in the form a+bia + bi, where aa is the real part and bibi is the imaginary part.

STEP 6

Evaluate statement D: "All whole numbers are positive integers."
Statement D is false. Whole numbers include all non-negative integers, which means they include 0 as well as positive integers. Therefore, not all whole numbers are positive integers.

STEP 7

Identify the false statement.
The false statements are B and D. Since we should identify the one false statement, we will consider statement B as the incorrect one based on the given context.

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