Practice and Problem-Solving Exercises

See Problem 1.

A Practice

Identify the hypothesis and conclusion of each conditional.

5. If you are an American citizen, then you have the right to vote.
6. If a figure is a rectangle, then it has four sides.
7. If you want to be healthy, then you should eat vegetables.

See Problem 2.

Write each sentence as a conditional.

8. Hank Aaron broke Babe Ruth's home-run record.
9. Algebra 33 − 7 = 14 33 minus , 7 equals , 14  implies that 3 x = 21 . 3 x equals , 21 .
10. Thanksgiving in the United States falls on the fourth Thursday of November.
11. A counterexample shows that a conjecture is false.
12. Coordinate Geometry A point in the first quadrant has two positive coordinates.

Write a conditional statement that each Venn diagram illustrates.

See Problem 3.

Determine if the conditional is true or false. If it is false, find a counterexample.

16. If a polygon has eight sides, then it is an octagon.
17. If you live in a country that borders the United States, then you live in Canada.
18. If you play a sport with a ball and a bat, then you play baseball.
19. If an angle measures 80, then it is acute.

See Problem 4.

If the given statement is not in if-then form, rewrite it. Write the converse, inverse, and contrapositive of the given conditional statement. Determine the truth value of all four statements. If a statement is false, give a counterexample.

20. If you are a quarterback, then you play football.
21. Pianists are musicians.
22. Algebra If 4 x + 8 = 28 , 4 x plus . 8 equals , 28 comma  then x = 5 . x equals , 5 .
23. Odd natural numbers less than 8 are prime.
24. Two lines that lie in the same plane are coplanar.

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