Answer :
Let's evaluate each statement and determine if it is true or false.
1. All natural numbers are whole numbers.
- Natural numbers are the set of positive integers starting from 1 (i.e., 1, 2, 3, ...).
- Whole numbers include all natural numbers and additionally the number 0.
- Therefore, every natural number is a whole number.
- This statement is true.
2. Sum of two negative integers is always a negative integer.
- When you add two negative integers, the result is always negative (e.g., -1 + -2 = -3).
- This statement is true.
3. All whole numbers are integers.
- Whole numbers are 0, 1, 2, 3, ... and so forth.
- Integers include all whole numbers together with their negative counterparts (e.g., -3, -2, -1, 0, 1, 2, 3, ...).
- So each whole number is indeed an integer.
- This statement is true.
4. Sum of a negative number and a positive number is always a positive number.
- The sum of a negative number and a positive number depends on their absolute values.
- For example, -3 + 5 is positive, but -5 + 3 is negative.
- This statement is false.
5. Product (or multiplication) of two negative integers is always a positive integer.
- The product of two negative integers is always positive (e.g., (-2) * (-3) = 6).
- This statement is true.
6. For any integer [tex]\( x \)[/tex], [tex]\( x \div 0 = 0 \div x = 0 \)[/tex].
- Division by zero is undefined in mathematics, meaning [tex]\( x \div 0 \)[/tex] is not a valid operation.
- However, [tex]\( 0 \div x \)[/tex] is defined and equals zero if [tex]\( x \)[/tex] is non-zero.
- This statement is false.
In summary, evaluating the statements:
- Statement 1: True
- Statement 2: True
- Statement 3: True
- Statement 4: False
- Statement 5: True
- Statement 6: False
Therefore, the appropriate assessments for the given statements are:
```
[1, 2, 3, 4, 5, 6]
```
1. All natural numbers are whole numbers.
- Natural numbers are the set of positive integers starting from 1 (i.e., 1, 2, 3, ...).
- Whole numbers include all natural numbers and additionally the number 0.
- Therefore, every natural number is a whole number.
- This statement is true.
2. Sum of two negative integers is always a negative integer.
- When you add two negative integers, the result is always negative (e.g., -1 + -2 = -3).
- This statement is true.
3. All whole numbers are integers.
- Whole numbers are 0, 1, 2, 3, ... and so forth.
- Integers include all whole numbers together with their negative counterparts (e.g., -3, -2, -1, 0, 1, 2, 3, ...).
- So each whole number is indeed an integer.
- This statement is true.
4. Sum of a negative number and a positive number is always a positive number.
- The sum of a negative number and a positive number depends on their absolute values.
- For example, -3 + 5 is positive, but -5 + 3 is negative.
- This statement is false.
5. Product (or multiplication) of two negative integers is always a positive integer.
- The product of two negative integers is always positive (e.g., (-2) * (-3) = 6).
- This statement is true.
6. For any integer [tex]\( x \)[/tex], [tex]\( x \div 0 = 0 \div x = 0 \)[/tex].
- Division by zero is undefined in mathematics, meaning [tex]\( x \div 0 \)[/tex] is not a valid operation.
- However, [tex]\( 0 \div x \)[/tex] is defined and equals zero if [tex]\( x \)[/tex] is non-zero.
- This statement is false.
In summary, evaluating the statements:
- Statement 1: True
- Statement 2: True
- Statement 3: True
- Statement 4: False
- Statement 5: True
- Statement 6: False
Therefore, the appropriate assessments for the given statements are:
```
[1, 2, 3, 4, 5, 6]
```
