Geometry
Problem Set - Conditionals
Name
Underline the hypothesis, and circle the conclusion of each conditional statement.
1. If the anchor gets loose, then the boat will drift.
2. If you study hard, then you will make a good grade on the test.
3. If 3𝑥 − 10 = 23, then 𝑥 = 11.
Write each statement in if-then form.
4. A deer is albino if it has white fur and pink eyes.
5. When it rains, it pours.
Write the converse, inverse, and contrapositive of each conditional statement and give the symbolic
form.
6. If it is Saturday, then school is closed.
Converse:
Symbolic Form:
Inverse:
Symbolic Form:
Contrapositive:
Symbolic Form:
Given the symbolic form, translate into a verbal statement. State whether it is the converse, inverse,
or contrapositive.
7.
Hypothesis: 𝑥 is odd
~𝒒 → ~𝒑:
𝒒 → 𝒑:
~𝒑 → ~𝒒:
Conclusion: 3𝑥 is odd.
Decide whether the statement is true or false. If false, give a counterexample.
8. If it is Friday night, then I will go to the football game.
9. If I made honor roll last semester, then my GPA was 3.6 or higher.
Write the converse of each of the following conditional statements. Determine whether the statement
and its converse are true. If possible, write the biconditional. If not possible, explain why.
10. If water is frozen, then its temperature is below 0° 𝐶 .
Converse:
Biconditional:
11. If my phone is an I-phone, then it is a smartphone.
Converse:
Biconditional:
Rewrite the biconditional statement as a conditional statement and its converse.
12. Two lines are parallel if and only if they do not intersect.
Conditional:
Converse:
Let p represent “Math is fun”, and let q represent “Math is difficult. Translate each of the following.
(Use ∧ for “and” , ∨ for “or”).
13. Math is not fun. _______________
14. Math is fun or math is difficult. _______________
15. Math is not fun and math is difficult. _______________
16. ~𝑞 → 𝑝