Practice worksheet on conditional statements in logic, featuring exercises to identify hypotheses and conclusions, rewrite statements in if-then form, and analyze a Venn diagram.

Let's go through each problem on the worksheet step by step, solving and explaining each one.

---

Understanding Conditional Statements

A conditional statement is in the form:
"If p, then q."
- Hypothesis (p): The part after "if" — what is assumed to be true.
- Conclusion (q): The part after "then" — what follows from the hypothesis.

A conditional statement is false only when:
- The hypothesis is true, and
- The conclusion is false.

---

## Problems 1–2: Identify Hypothesis and Conclusion

1. If you can see the stars, then it is night.

- Hypothesis: You can see the stars.
*(This comes after "if")*
- Conclusion: It is night.
*(This comes after "then")*

✔ Answer:
- Hypothesis: You can see the stars
- Conclusion: It is night

---

2. If x is an even number, then x is divisible by 2.

- Hypothesis: x is an even number
- Conclusion: x is divisible by 2

✔ Answer:
- Hypothesis: x is an even number
- Conclusion: x is divisible by 2

---

## Problems 3–5: Write a Conditional Statement

We need to rewrite each statement in "If p, then q" form.

---

3. Three noncollinear points determine a plane.

We rephrase this as a conditional:

> If three points are noncollinear, then they determine a plane.

✔ Answer:
*If three points are noncollinear, then they determine a plane.*

---

4. Congruent segments have equal measures.

Rewrite in if-then form:

> If two segments are congruent, then they have equal measures.

✔ Answer:
*If two segments are congruent, then they have equal measures.*

---

5. On Tuesday, play practice is at 6:00.

This is not in conditional form yet. We can interpret it as:

> If it is Tuesday, then play practice is at 6:00.

✔ Answer:
*If it is Tuesday, then play practice is at 6:00.*

---

6. Venn Diagram: Insects and House Fly

The diagram shows:
- A large oval labeled Insects
- A smaller oval inside it labeled House Fly

This means: All house flies are insects, but not all insects are house flies.

So we can write a conditional statement based on set inclusion:

> If something is a house fly, then it is an insect.

✔ Answer:
*If it is a house fly, then it is an insect.*

---

## Problems 7–8: Use the Conditional Statement

Given:
"If it is a bicycle, then it has two wheels."

7. Give the hypothesis of the conditional statement.

- The hypothesis is the part after "if".

✔ Answer:
*It is a bicycle*

---

8. Give the conclusion of the conditional statement.

- The conclusion is the part after "then".

✔ Answer:
*It has two wheels*

---

## ✔ Final Answers Summary:

1.

- Hypothesis: You can see the stars
- Conclusion: It is night

2.

- Hypothesis: x is an even number
- Conclusion: x is divisible by 2

3.

*If three points are noncollinear, then they determine a plane.*

4.

*If two segments are congruent, then they have equal measures.*

5.

*If it is Tuesday, then play practice is at 6:00.*

6.

*If it is a house fly, then it is an insect.*

7.

*It is a bicycle*

8.

*It has two wheels*

---

Let me know if you'd like this formatted for printing or want explanations for truth values or related concepts!