Question

identify the hypothesis and conclusion of each conditional.

1. if you are an american citizen, then you have the right to vote.
2. if a figure is a rectangle, then it has four sides.
3. if you want to be healthy, then you should eat vegetables.

write each sentence as a conditional.

1. a point in the first quadrant has two positive coordinates.
2. thanksgiving in the united states falls on the fourth thursday of november.

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

1. if you live in a country that borders the united states, then you live in canada.
2. if angle measures 80°, then it is acute.
3. if you play a sport with a ball and a bat, then you play baseball.

if the given statement is not in if - then form, rewrite it. write inverse, converse, contrapositive of the conditional statement. determine the truth value of all four statements and find a counterexample.

1. if you are a quarterback, then you play football.

inverse:
converse:
contrapositive:

1. pianists are musicians.

conditional:

Explanation:

1. Hypothesis: You are an American citizen. Conclusion: You have the right to vote.
2. Hypothesis: A figure is a rectangle. Conclusion: It has four sides.
3. Hypothesis: You want to be healthy. Conclusion: You should eat vegetables.
4. Conditional: If a point is in the first quadrant, then it has two positive coordinates.
5. Conditional: If it is Thanksgiving in the United States, then it falls on the fourth Thursday of November.
6. False. Counter - example: Mexico also borders the United States.
7. True. An acute angle is defined as an angle with measure less than 90°.
8. False. Counter - example: Cricket is a sport with a ball and a bat.
9. Inverse: If you are not a quarterback, then you do not play football. (False, as there are other positions in football). Converse: If you play football, then you are a quarterback. (False, as there are other positions). Contrapositive: If you do not play football, then you are not a quarterback. (True).
10. Conditional: If a person is a pianist, then the person is a musician. Inverse: If a person is not a pianist, then the person is not a musician. (False, could be other types of musicians). Converse: If a person is a musician, then the person is a pianist. (False, could be other types of musicians). Contrapositive: If a person is not a musician, then the person is not a pianist. (True).

Answer:

1. Hypothesis: You are an American citizen. Conclusion: You have the right to vote.
2. Hypothesis: A figure is a rectangle. Conclusion: It has four sides.
3. Hypothesis: You want to be healthy. Conclusion: You should eat vegetables.
4. If a point is in the first quadrant, then it has two positive coordinates.
5. If it is Thanksgiving in the United States, then it falls on the fourth Thursday of November.
6. False, Mexico
7. True
8. False, Cricket
9. Inverse: If you are not a quarterback, then you do not play football. (False) Converse: If you play football, then you are a quarterback. (False) Contrapositive: If you do not play football, then you are not a quarterback. (True)
10. Conditional: If a person is a pianist, then the person is a musician. Inverse: If a person is not a pianist, then the person is not a musician. (False) Converse: If a person is a musician, then the person is a pianist. (False) Contrapositive: If a person is not a musician, then the person is not a pianist. (True)