Final answer:
The original statement, 'If a number is a natural number, then it is also a whole number' is true because every natural number falls into the set of whole numbers. However, its converse is not true, as whole numbers include 0, which is not a natural number, making the inverse and the bi-conditional false. The contrapositive of the statement is true, maintaining logical consistency.
Step-by-step explanation:
If a number is a natural number, then it is indeed also a whole number. The relationship between natural numbers and whole numbers is an inclusive one, where all natural numbers (1, 2, 3, ...) are also whole numbers (0, 1, 2, 3, ...). The original statement can be expressed in logical form as: If P, then Q, where P is 'a number is a natural number,' and Q is 'it is also a whole number.'
Here is how the other forms of the statement look:
The inverse negates both the hypothesis and the conclusion: If not P, then not Q. So, 'If a number is not a natural number, then it is not a whole number.'
The converse switches the hypothesis and the conclusion: If Q, then P. For our statement, 'If a number is a whole number, then it is also a natural number.'
The contrapositive negates and switches the hypothesis and conclusion: If not Q, then not P. Therefore, 'If a number is not a whole number, then it is not a natural number.'
The bi-conditional states that P if and only if Q: A number is a natural number if and only if it is a whole number.'
The truth value of the original statement is true since all natural numbers are whole numbers. However, the converse is not true because whole numbers also include 0, which is not a natural number. Consequently, the inverse and the bi-conditional are false. The contrapositive is true because if it is not a whole number, then it can't be a natural number (considering that whole numbers include all natural numbers).