Student worksheet on conditional statements in logic and proof, including identifying parts of statements and writing them in if-then form.

Problem Analysis:

The image shows a worksheet titled "Unit 2: Logic & Proof, Homework 3: Conditional Statements." The tasks involve identifying the hypothesis and conclusion of conditional statements and rewriting statements in if-then form. Additionally, there are questions about writing inverses, converses, contrapositives, and biconditionals of given statements.

Solution Explanation:

#### Part 1: Identify the Hypothesis and Conclusion
1. Statement: If the product of two numbers is 0, then at least one of the numbers must be 0.
- Hypothesis: The product of two numbers is 0.
- Conclusion: At least one of the numbers must be 0.

2. Statement: If it is daylight saving time, then I must reset my clocks.
- Hypothesis: It is daylight saving time.
- Conclusion: I must reset my clocks.

#### Part 2: Write the Following Statements in If-Then Form
3. Statement: A rhombus is a quadrilateral with four congruent sides.
- If-Then Form: If a figure is a rhombus, then it is a quadrilateral with four congruent sides.

4. Statement: Those that finish the marathon will get a medal.
- If-Then Form: If you finish the marathon, then you will get a medal.

#### Part 3: Write the Inverse, Converse, Contrapositive, and Biconditional
5. Statement: If you buy a Coke, then you pay less than $2.
- Inverse: If you do not buy a Coke, then you do not pay less than $2.
- Truth Value: False (You might still pay less than $2 for something else.)
- Converse: If you pay less than $2, then you buy a Coke.
- Truth Value: False (You might pay less than $2 for something other than a Coke.)
- Contrapositive: If you do not pay less than $2, then you do not buy a Coke.
- Truth Value: True (If you pay $2 or more, you cannot be buying a Coke under this condition.)
- Biconditional: You buy a Coke if and only if you pay less than $2.
- Truth Value: False (Buying a Coke does not necessarily mean you pay less than $2, and paying less than $2 does not necessarily mean you bought a Coke.)

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{1. Hypothesis: The product of two numbers is 0.} \\
\text{ Conclusion: At least one of the numbers must be 0.} \\
\text{2. Hypothesis: It is daylight saving time.} \\
\text{ Conclusion: I must reset my clocks.} \\
\text{3. If a figure is a rhombus, then it is a quadrilateral with four congruent sides.} \\
\text{4. If you finish the marathon, then you will get a medal.} \\
\text{5. Inverse: If you do not buy a Coke, then you do not pay less than $2. (False)} \\
\text{ Converse: If you pay less than $2, then you buy a Coke. (False)} \\
\text{ Contrapositive: If you do not pay less than $2, then you do not buy a Coke. (True)} \\
\text{ Biconditional: You buy a Coke if and only if you pay less than $2. (False)}
\end{array}
}
\]