Logic worksheet focusing on conditional statements and their components.

Let's go through each question step by step and solve them with explanations.

---

1. Draw a line to connect the word *hypothesis* to the conditional statements hypothesis.

Statement:
*If the weatherman is correct, then school will be cancelled.*

In a conditional statement of the form:
If P, then Q,
- P is the hypothesis (the "if" part),
- Q is the conclusion (the "then" part).

So in this case:
- Hypothesis: *"the weatherman is correct"*
- Conclusion: *"school will be cancelled"*

✔ Answer: Connect the word hypothesis to "the weatherman is correct".

---

2. Which option is the inverse to the conditional statement?

Original statement:
*If Joe scores an 87% on his quiz, then he will get a B on his report card.*

This is:
If P, then Q
Where:
- P = Joe scores an 87%
- Q = He gets a B

The inverse is formed by negating both the hypothesis and conclusion:
If not P, then not Q

So:
*If Joe does NOT score an 87%, then he will NOT get a B.*

Now let’s examine the choices:

A. If Joe does not score an 87% on his quiz, then he will not get a B on his report card.
→ This matches the inverse. ✔

B. If Joe gets a B on his report card, then he scored an 87% on his quiz.
→ This is the converse (Q → P). ✘

C. If Joe does not get a B on his report card, then he did not score an 87% on his quiz.
→ This is the contrapositive (not Q → not P). ✘

✔ Correct Answer: A

---

3. Which option is the contrapositive to the conditional statement?

Original statement:
*If the Varsity team wins Friday night, then they will be 3–0.*

This is:
If P, then Q
- P = Varsity team wins Friday night
- Q = They are 3–0

The contrapositive is:
If not Q, then not P
→ *If they are NOT 3–0, then they did NOT win Friday night.*

Check options:

A. If the Varsity team does not win Friday night, then they will not be 3-0.
→ This is the inverse (not P → not Q). ✘

B. If the Varsity team is 3-0, then they won Friday night.
→ This is the converse (Q → P). ✘

C. If the Varsity team is not 3-0, then they did not win Friday night.
→ This is not Q → not P → the contrapositive. ✔

✔ Correct Answer: C

---

4. Which option is the converse to the conditional statement?

Original statement:
*If Amber works 5 days this week, then she will have enough money to go to the beach next week.*

This is:
If P, then Q
- P = Amber works 5 days
- Q = She has enough money

The converse swaps the hypothesis and conclusion:
If Q, then P
→ *If Amber has enough money to go to the beach, then she worked 5 days.*

Check options:

A. If Amber does not work 5 days, then she will not have enough money.
→ This is the inverse (not P → not Q). ✘

B. If Amber has enough money to go to the beach next week, then she worked 5 days this week.
→ This is Q → P → the converse. ✔

C. If Amber does not have enough money, then she did not work 5 days.
→ This is the contrapositive (not Q → not P). ✘

✔ Correct Answer: B

---

5. Draw a line to connect the word *conclusion* to the conditional statements conclusion.

Statement:
*If Brendon passes his test, then he will spend the night at a friend's.*

Again, in If P, then Q:
- P = Brendon passes his test → hypothesis
- Q = He will spend the night at a friend's → conclusion

✔ Answer: Connect the word conclusion to "he will spend the night at a friend's"

---

✔ Final Answers Summary:

1. Connect "hypothesis" to "the weatherman is correct"
2. A – Inverse
3. C – Contrapositive
4. B – Converse
5. Connect "conclusion" to "he will spend the night at a friend's"

Let me know if you'd like a visual version or printable answers!