Title: Lesson 7
Course: quiz duplicate error

Q: Identify the hypothesis and conclusion of this conditional statement:
If yesterday was Friday, then today is Saturday.
- Hypothesis: Yesterday was Friday. Conclusion: Today is not Saturday.
- Hypothesis: Today is not Saturday. Conclusion: Yesterday was Friday.
- Hypothesis: Today is Saturday. Conclusion: Yesterday was Friday.
- Hypothesis: Yesterday was Friday. Conclusion: Today is Saturday.
A: Hypothesis: Yesterday was Friday. Conclusion: Today is Saturday.

Q: Identify the hypothesis and conclusion of this conditional statement:
If tomorrow is Thursday, then yesterday was Tuesday.
- Hypothesis: Yesterday was not Tuesday. Conclusion: Tomorrow is Thursday.
- Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was not Tuesday.
- Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.
- Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday.
A: Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.

Q: Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
- Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles.
- Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.
- Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles.
- Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular.
A: Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.

Q: Write this statement as a conditional in if-then form:
All triangles have three sides.
- If a triangle has three sides, then all triangles have three sides.
- If a figure has three sides, then it is not a triangle.
- If a figure is a triangle, then all triangles have three sides.
- If a figure is a triangle, then it has three sides.
A: If a figure is a triangle, then it has three sides.

Q: Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
- Sara Lucas lives in Springfield.
- Jonah Lincoln lives in Springfield, Illinois.
- Billy Jones lives in Chicago, Illinois.
- Erin Naismith lives in Springfield, Massachusetts.
A: Erin Naismith lives in Springfield, Massachusetts.

Q: Draw a Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ and the part following then is the ____.
- conditional; conclusion; hypothesis
- hypothesis; conclusion; conditional
- conditional; hypothesis; conclusion
- hypothesis; conditional; conclusion
A: conditional; hypothesis; conclusion

Q: Which choice shows a true conditional with the hypothesis and conclusion identified correctly?
- If tomorrow is Monday, then yesterday was Saturday. Hypothesis: Yesterday was Saturday. Conclusion: Tomorrow is Monday.
- Yesterday was Saturday if tomorrow is Monday. Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was Saturday.
- Yesterday was Sunday if tomorrow is Monday. Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was Sunday.
- If tomorrow is Monday, then yesterday was Saturday. Hypothesis: Yesterday was Saturday. Conclusion: Tomorrow is not Monday.
A: Yesterday was Saturday if tomorrow is Monday. Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was Saturday.
Partly right: Yesterday was Sunday if tomorrow is Monday. Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was Sunday. (50%)

Q: Which choice shows a true conditional with the hypothesis and conclusion identified correctly?
- Two lines are perpendicular if the lines intersect at right angles. Hypothesis: Two lines intersect at right angles. Conclusion: Two lines are perpendicular.
- If two lines intersect at right angles, then the two lines are perpendicular. Hypothesis: Two lines are perpendicular. Conclusion: Two lines intersect at right angles.
- If two lines intersect at right angles, then the two lines are perpendicular. Hypothesis: Two lines are perpendicular. Conclusion: Two lines do not intersect at right angles.
- Two lines are parallel if the lines intersect at right angles. Hypothesis: Two lines intersect at right angles. Conclusion: Two lines are parallel.
A: Two lines are perpendicular if the lines intersect at right angles. Hypothesis: Two lines intersect at right angles. Conclusion: Two lines are perpendicular.

Q: Which choice shows a true conditional with the hypothesis and conclusion identified correctly?
- If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is not Thursday.
- Yesterday was Tuesday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.
- If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday.
- Yesterday was Monday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Monday.
A: Yesterday was Tuesday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.

Q: What is the conclusion of the following conditional?
A number is divisible by 9 if the sum of the digits of the number is divisble by 9.
- The number is odd.
- The sum of the digits of the number is divisble by 9.
- If the sum of the digits of a number is divisble by 9, then the number is divisible by 9.
- The number is divisible by 9.
A: The number is divisible by 9.

Q: What is the conclusion of the following conditional?
A number is divisible by 5 if the number ends with digits 0 or 5.
- The number is divisible by 5.
- The number is odd.
- The number ends with digits 0 or 5.
- If a number ends with the digit 0 or 5, then the number is divisible by 5.
A: The number is divisible by 5.

Q: What is the conclusion of the following conditional?
A number is divisible by 2 if the number is even.
- If a number is even, then the number is divisible by 2.
- The number is divisible by 2.
- The number is even.
- The number is even.
A: The number is divisible by 2.

Q: What is the converse of the following conditional?
If a number is divisible by 6, then it is divisible by 2.
- If a number is divisible by 6, then it is divisible by 2.
- If a number is not divisible by 2, then it is not divisible by 6.
- If a number is not divisible by 6, then the number is not divisible by 2.
- If a number is divisible by 2, then it is divisible by 6.
A: If a number is divisible by 2, then it is divisible by 6.

Q: What is the converse of the following conditional?
If a number is divisible by 10, then it is divisible by 5.
- If a number is not divisible by 10, then a number is not divisible by 5.
- If a number is divisible by 10, then it is divisible by 5.
- If a number is divisible by 5, then it is divisible by 10.
- If a number is not divisible by 5, then it is not divisible by 10.
A: If a number is divisible by 5, then it is divisible by 10.

Q: What is the converse of the following conditional?
If a number is a natural number, then it is a whole number.
- If a number is a whole number, then it is a natural number.
- If a number is a natural number, then it is a whole number.
- If a number is not a whole number, then it is not a natural number.
- If a number is not a natural number, then it is not a whole number.
A: If a number is a whole number, then it is a natural number.

Q: What is the converse and the truth value of the converse of the following conditional?
If an angle is a right angle, then its measure is 90.
- If an angle is not a right angle, then its measure is 90. False
- If an angle is not a right angle, then its measure is not 90. True
- If an angle has measure 90, then it is a right angle. False
- If an angle has measure 90, then it is a right angle. True
A: If an angle has measure 90, then it is a right angle. True

Q: Which conditional has the same truth value as its converse?
- If x = 7, then [Image].
- If a figure is a square, then it has four sides.
- If x – 17 = 4, then x = 21.
- If an angle has measure 80, then it is acute.
A: If x – 17 = 4, then x = 21.

Q: For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 5, then x^2 = 25.
- If x^2 = 25, then x = 5. True; x = 5 if and only if x^2 = 25.
- If x^2 = 25, then x = 5. True; x^2 = 25 if and only if x = 5.
- If x^2 = 25, then x = 5. False
- If x^2 = 5, then x = 25. False
A: If x^2 = 25, then x = 5. False

Q: For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 4, then x^2 = 16.
- If x^2 = 16, then x = 4. False
- If x^2 = 16, then x = 4. True; x^2 = 16 if and only if x = 4.
- If x^2 = 16, then x = 4. True; x = 4 if and only if x^2 = 16.
- If x^2 = 4, then x = 16. False
A: If x^2 = 16, then x = 4. False
Partly right: If x^2 = 16, then x = 4. True; x^2 = 16 if and only if x = 4. (50%); If x^2 = 16, then x = 4. True; x = 4 if and only if x^2 = 16. (50%)

Q: For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 8, then x^2 = 64.
- If x^2 = 64, then x = 8. False
- If x^2 = 8, then x = 64. False
- If x^2 = 64, then x = 8. True; x^2 = 64 if and only if x = 8.
- If x^2 = 64, then x = 8. True; x = 8 if and only if x^2 = 64.
A: If x^2 = 64, then x = 8. False

Q: Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.
- One statement is false. If two lines do not intersect, they could be skew..
- One statement is false. If two lines are parallel, they may intersect twice.
- Both statements are true. Two lines are parallel if and only if they do not intersect.
- Both statements are true. Two lines are not parallel if and only if they do not intersect.
A: One statement is false. If two lines do not intersect, they could be skew.. / Both statements are true. Two lines are parallel if and only if they do not intersect.

Q: Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.
If an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
- One statement is false. If an angle measure is 90, the angle may be a vertical angle.
- One statement is false. If an angle is a right angle, its measure may be 180.
- Both statements are true. An angle is a right angle if and only if its measure is 90.
- Both statements are true. The measure of angle is 90 if and only if it is not a right angle.
A: Both statements are true. An angle is a right angle if and only if its measure is 90.

Q: Write the two conditional statements that make up the following biconditional.
I drink juice if and only if it is breakfast time.
- I drink juice if and only if it is breakfast time. It is breakfast time if and only if I drink juice.
- If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice.
- If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time.
- I drink juice. It is breakfast time.
A: If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice.

Q: When a conditional and its converse are true, you can combine them as a true ____.
- counterexample
- biconditional
- unconditional
- hypothesis
A: biconditional

Q: Which statement provides a counterexample to the following faulty definition?
A square is a figure with four congruent sides.
- A six-sided figure can have four sides congruent.
- Some triangles have all sides congruent.
- A square has four congruent angles.
- A rectangle has four sides.
A: A six-sided figure can have four sides congruent.

Q: Which conditional has the same truth value as its converse? (Find the statement where both the conditional and the converse are true)
- If x = 7, then [Image].
- If a figure is a square, then it has four sides.
- If x – 17 = 4, then x = 21.
- If an angle has measure 80, then it is acute.
A: If x – 17 = 4, then x = 21.

Q: For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 5, then x^2 = 25.
- If x^2 = 25, then x = 5. True; x = 5 if and only if x^2 = 25. (If x^2=25, then x could equal 5 or -5.)
- If x^2 = 25, then x = 5. True; x^2 = 25 if and only if x = 5. (If x^2=25, then x could equal 5 or -5.)
- If x^2 = 25, then x = 5. False
- If x^2 = 5, then x = 25. False
A: If x^2 = 25, then x = 5. False
Partly right: If x^2 = 25, then x = 5. True; x = 5 if and only if x^2 = 25. (50%); If x^2 = 25, then x = 5. True; x^2 = 25 if and only if x = 5. (50%)

Q: For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 8, then x^2 = 64.
- If x^2 = 64, then x = 8. False
- If x^2 = 8, then x = 64. False
- If x^2 = 64, then x = 8. True; x^2 = 64 if and only if x = 8. (If x^2=64, then x could equal 8 or -8.)
- If x^2 = 64, then x = 8. True; x = 8 if and only if x^2 = 64. (If x^2=64, then x could equal 8 or -8.)
A: If x^2 = 64, then x = 8. False
Partly right: If x^2 = 64, then x = 8. True; x^2 = 64 if and only if x = 8. (50%); If x^2 = 64, then x = 8. True; x = 8 if and only if x^2 = 64. (50%)