Name: _______________________________ Date: ______________

UNIT 1 PRACTICE TEST: INTRODUCTION TO PROOFS & LOGIC

GEOMETRY, FALL 2011, MR. CARLBERG

1. Prove that and are complementary, i.e. their measures add up to 90 degrees.

2. Prove that .

𝑥

𝑦

𝑎

𝑏

𝑐

3. Provide counterexamples to prove each statement false. Show or explain why it is a

counterexample.

a) For any number x, the value of x2 is greater than the value of x.

b) If x is a prime number, then x + 1 is not a prime number.

c) If two angles are supplementary, they are both right angles.

4. Consider the following statements whose truth values you can determine.

5. Let p and q be true statements and r and s be false statements. State the truth value of the

following statements

a) (p q) r

b) (~r → s) → ~p

c) (q r → p) (p → q r)

6. Consider the statement: “If Obama succeeds, all Americans succeed.” Write the statements

(a) inverse, (b) converse, and (c) contrapositive.

7. Are the statements ~(p q) and ~p ~q logically equivalent? Use a truth table to justify your

answer.

8. Derive the truth table for the statement (p → q) (q → p).