Question

TRUE OR FALSE

There are whole numbers that are not integers.

There are rational numbers that are not whole
numbers.

All rational numbers are integers.

All whole numbers are rational numbers.

Answer 1

Addressing the statements about number types, we find that whole numbers are indeed integers, rational numbers include non-whole numbers, rational numbers are not all integers but include integers, and all whole numbers are also rational numbers. These truths are based on the properties and relationships defined within mathematical systems.

Step-by-step explanation:

Understanding Number Types and Their Relationships

While assessing the statements given, we must remember that different types of numbers have distinct characteristics in mathematics. Here are the statements explored:

1. There are whole numbers that are not integers. This statement is false. All whole numbers are integers because the set of whole numbers is a subset of the integers. Whole numbers are the set of non-negative integers, which include 0, 1, 2, 3, and so forth.
2. There are rational numbers that are not whole numbers. This statement is true. Rational numbers include all numbers that can be expressed as a fraction or ratio of two integers, where the denominator is not zero. This includes fractions like 1/2 or -3/4, which are not whole numbers.
3. All rational numbers are integers. This statement is false. The correct statement should be that all integers are rational numbers. An integer can be expressed as a ratio where the denominator is 1, but rational numbers can also include fractions and decimals that are not whole numbers.
4. All whole numbers are rational numbers. This statement is true. Since whole numbers can be expressed as a ratio of themselves to 1 (for example, 2 can be written as 2/1), they fall within the category of rational numbers.

The exploration of these statements emphasizes how intuition in mathematics is based on the defined properties and relationships of numbers.

Answer 2

1. False. All whole numbers are integers.
2. True. For example, 1/2 is a rational number but it is not a whole number.
3. False. For example, 2/7 is a rational number but not an integer.
4. True. Each and every whole numbers are rational numbers.

ANSWERS:

`1. False \\ 2. True \\ 3. False \\ 4. True \\`

Hope you could get an idea from here.

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