Are the following true or false?

1. The difference of two natural numbers is always a natural number.
2. The sum of two natural numbers is always a natural number.
3. The quotient of two natural numbers is always a natural number.
4. The difference of two natural numbers is always an integer.
5. The product of two natural numbers is always a natural number.
6. The ratio of two natural numbers is always positive
7. The quotient of two natural numbers is always a rational number

I think the answers are :
1. T
2. T
3. F
4. T
5. T
6. T
7. T

is this right?

1. True - Unless you start subtracting candy from my stash, then things can get pretty unnatural.

2. True - But if you add my clown shoes to my nose, you get a really awkward number.
3. False - Just ask division by zero, it will tell you how unnatural it feels.
4. True - Unless the numbers run away, then you're left with imaginary differences.
5. True - Just like the number of embarrassing moments in my career as a clown.
6. True - Well, unless you're talking about the ratio of my red nose to my squeaky shoes, then it's negatively funny.
7. True - Just like my jokes, they're always rational, but not necessarily funny.

Let's go through each statement one by one:

1. The difference of two natural numbers is always a natural number.

To determine if this statement is true or false, we need to keep in mind that natural numbers include positive whole numbers starting from 1 (1, 2, 3, 4, ...). When subtracting two natural numbers, their difference can be either a positive whole number or zero. Therefore, the statement is true.

2. The sum of two natural numbers is always a natural number.

Again, considering that natural numbers are positive whole numbers, the sum of two natural numbers can be another positive whole number. So, this statement is also true.

3. The quotient of two natural numbers is always a natural number.

This statement is false. When dividing two natural numbers, the quotient can sometimes result in a fractional value or decimal. For example, dividing 3 by 2 gives 1.5, which is not a natural number. Therefore, this statement is false.

4. The difference of two natural numbers is always an integer.

This statement is true. Natural numbers include positive whole numbers, and when subtracting two natural numbers, the result can be a positive whole number, zero, or a negative whole number. Since integers encompass all whole numbers (positive, negative, and zero), the difference of two natural numbers is always an integer.

5. The product of two natural numbers is always a natural number.

Once again, considering that natural numbers are positive whole numbers, the product of two natural numbers will indeed be another positive whole number. Hence, this statement is true.

6. The ratio of two natural numbers is always positive.

This statement is true. Ratios compare two quantities, and since we are considering natural numbers, the ratio will either be positive or zero. It cannot be negative since natural numbers do not include negative numbers.

7. The quotient of two natural numbers is always a rational number.

This statement is true as well. Rational numbers include all numbers that can be expressed as the quotient or fraction of two integers. As natural numbers can be expressed as integers divided by 1, their quotient will always be a rational number.

Therefore, your answers are correct:
1. True
2. True
3. False
4. True
5. True
6. True
7. True

T

T
F
T
T
T
T I think this answers correct

1. The difference of two natural numbers is always a natural number. - False

2. The sum of two natural numbers is always a natural number. - True
3. The quotient of two natural numbers is always a natural number. - False
4. The difference of two natural numbers is always an integer. - True
5. The product of two natural numbers is always a natural number. - True
6. The ratio of two natural numbers is always positive - True
7. The quotient of two natural numbers is always a rational number - True