Logic Review Sheet
Use the following conjecture for questions 1-4: “All successful decathletes run fast, jump high,
and throw far.”
1. Rewrite the conjecture as a conditional statement.
2. Identify the hypothesis of the conditional statement you wrote in question 1.
3. Identify the conclusion of the conditional statement you wrote in question 1.
4. Rewrite the conjecture as a biconditional statement.
For questions 5-7 use the following conditional: “If you upset the Geometry teachers right
before your test, then your test will be harder.”
5. Write the inverse.
6. Write the contrapositive.
7. Write the converse.
Use the following conjecture for questions 8-14: “Military families don’t live in one place for
very long.”
8. Rewrite the conjecture as a conditional statement.
9. Identify the hypothesis of the conditional statement from question 8.
10. Identify the conclusion of the conditional statement from question 8.
11. Write the contrapositive of the conditional statement from question 8.
12. Write the converse of the conditional statement from question 8.
13. Write the inverse of the conditional statement from question 8.
14. Rewrite the conjecture as a biconditional statement.
Answer questions 15-21 in a complete sentence.
15. How do you rewrite a conjecture as a conditional statement?
16. How do you write the converse of a conditional statement?
17. How do you write the inverse of a conditional statement?
18. How do you write the contrapositive of a conditional statement?
19. How do you rewrite a conjecture as a biconditional statement?
20. What pairs of statements must have the same truth value?
21. What two statements must be true in order for a biconditional statement to be true?
For questions 22-26, let
p​ = the clock is 15 minutes behind
q = you lost your car keys
r = Marco misses his game
s = you are not late
22. What statement represents the converse of ~ p → q ?
23. What statement is represented by ​q → ~s​?
24. What statement is represented by r ↔ q​?
25. What statement is represented by p ⋀ q ∴ ~​s​?
26. What statement is represented by q ⋁ p → r ?
Give a valid conclusion, if possible, and state the law used in questions 27-36.
27. If you have a tattoo, then you must cover it at work.
Braydon has a tattoo.
28. If the volume is loud on the tv, then you will get a headache.
Olivia got a headache.
29. If you haven’t had Moo Thru ice cream, then you are missing out.
If you live far from Bealeton, then you haven’t had Moo Thru ice cream.
30. If you drop the calculator, then it will break.
If the calculator breaks, then we will not be able to have nice things.
31. If it is summer, then people vacation at the beach.
If it is summer, then the weather is more humid.
32. If the sky turns dark, then the snow will come.
If the snow comes, then the roads will be treacherous.
If the roads become treacherous, then we will not have to come to school.
33. If your friend is late, then you start to worry.
If your friend oversleeps, then they will be late.
34. If you drink a lot of water, then you will have to use the restroom frequently.
If you have to use the restroom frequently, then you will annoy your teacher.
35. If your favorite animal is the same as your best friend’s, then your favorite is a llama.
Your best friend’s favorite animal is the same as yours.
36. If you live in Warrenton, then you live in Virginia.
If you live in Fauquier County, then you live in Virginia.