Question

Choose which statement is not equivalent.? If a number is whole, then it is a rational number.

1. All whole numbers are rational numbers
2. A number is rational, if it is a whole number.
3. Being whole is sufficient for being rational.
4. A number is rational, only if it is whole.

Answer 1

Statement 4, which says that a number is rational only if it is whole, is not equivalent to the others.

Step-by-step explanation:

To determine which statement is not equivalent, we need to analyze each statement individually.

1. Statement 1: This statement is equivalent to saying that all whole numbers are rational numbers. This is true because all whole numbers can be written as fractions where the denominator is 1.
2. Statement 2: This statement is equivalent to saying that if a number is a whole number, then it is a rational number. This is also true because a whole number can be written as a fraction (e.g., 7 can be written as 7/1).
3. Statement 3: This statement is equivalent to saying that being whole is sufficient for being rational. This is true because if a number is a whole number, then it can be written as a fraction with a denominator of 1.
4. Statement 4: This statement is not equivalent to the others. It says that a number is rational only if it is whole, which is not true. There are rational numbers that are not whole numbers, such as 1/2 or 3/4.

Therefore, the correct answer is statement 4.