What would make this statements False.
The opposite of each natural number is a natural number.
There is no whole number that has an opposite that is a whole number.
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What would make this statements False.
The opposite of each natural number is a natural number.
There is no whole number that has an opposite that is a whole number.
To make the first statement false, you would need to find a natural number whose opposite is not a natural number. However, in the set of natural numbers (positive integers greater than or equal to 1), every number does not have an opposite that is also a natural number. Therefore, the first statement is true, not false.
To make the second statement false, you would need to find a whole number that has an opposite that is also a whole number. This is possible, as any positive or negative whole number has an opposite that is also a whole number. Therefore, the second statement is true, not false.
To determine what would make these statements false, we need to understand the concepts of natural numbers and their opposites.
1. The opposite of each natural number is a natural number:
The natural numbers consist of all positive integers starting from 1 (i.e., 1, 2, 3, 4, ...). The opposite of a number is obtained by changing its sign and making it negative. Therefore, the statement is true because for every natural number, its opposite is indeed a negative number, which is also a natural number.
2. There is no whole number that has an opposite that is a whole number:
Whole numbers include all natural numbers (i.e., positive integers) along with zero. An opposite number refers to a number that, when added to the original number, equals zero. In the case of whole numbers, only zero has no opposite, as adding any other whole number to it will not result in zero. Therefore, the statement is true because zero is the only whole number without an opposite within the set of whole numbers.
In summary, to make these statements false, we would need to find a natural number without a natural number as its opposite or find a whole number that has a whole number as its opposite. However, based on the definitions of natural numbers and whole numbers, these scenarios are not possible, so the statements remain true.