Question
Question 1
(Multiple Choice Worth 1 Points)
(01.05 MC)
What is the biconditional statement of the following conditional statement?
"If a polygon has six sides, then it is a hexagon."
If a polygon does not have six sides, then it is a not hexagon.
A polygon has six sides if and only if it is a hexagon.
If a polygon is a hexagon, then it has six sides.
If a polygon is not a hexagon, then it is does not have six sides.
Question 2
(Multiple Choice Worth 1 Points)
(01.05 MC)
What is the converse of the following statement?
"If the sum of the interior angles of a polygon is 180°, then the polygon is a triangle."
If the polygon is a triangle, then the sum of the interior angles of the polygon is 180°.
If the polygon is not a triangle, then the sum of interior angles of the polygon is not 180°.
If the sum of the interior angles of a polygon is not 180°, then the polygon is not a triangle.
If the sum of the interior angles of a polygon is 180°, then the triangle is a polygon.
Question 3
(Multiple Choice Worth 1 Points)
(01.05 LC)
What is the contrapositive of the following statement?
"If there is rain, then the dog will not bark."
If the dog will bark, then there is no rain.
If there is no rain, then the dog will not bark.
If the dog will not bark, then there is rain.
If there is no rain, then the dog will bark.
Question 4
(Multiple Choice Worth 1 Points)
(01.05 LC)
What is the inverse of the following statement?
"If a polygon does not have five sides, then the polygon is a rectangle."
If the polygon is a rectangle, then the polygon does not have five sides.
If the polygon is not a rectangle, then the polygon has five sides.
If the polygon does not have five sides, then the polygon is not a rectangle.
If the polygon has five sides, then the polygon is not a rectangle.
Question 5
(Multiple Choice Worth 1 Points)
(01.05 MC)
Jenni wrote a conditional statement and its converse.
Conditional: If angles are right angles, then the angles have the same measure.
Converse: If angles have the same measurement, then they are right angles.
Did Jenni write the converse statement properly? Determine if the converse is true or false and give a counterexample if the converse is false.
No; two angles that each measure 45°
Yes; two angles that each measure 90°
Yes; two angles that each measure 41°
No; two angles that each measure 82°
Question 6
(Multiple Choice Worth 1 Points)
(01.05 MC)
Read the following statements.
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg writes, "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."
Cassandra writes, "Statement 2 is the converse of statement 1 and inverse of statement 3."
Who is correct?
Both Meg and Cassandra are incorrect.
Only Meg is correct.
Both Meg and Cassandra are correct.
Only Cassandra is correct.
Question 7
(Multiple Choice Worth 1 Points)
(01.05 MC)
What is the converse of the following conditional statement?
"If it is sunny, then it is 80° Fahrenheit."
Determine if the converse is true or false and give a counterexample if the converse is false.
If it is sunny, then it is 80° Fahrenheit. The converse is true.
If it is 80° Fahrenheit, then it is sunny. The converse is true.
If it is not sunny, then it is not 80° Fahrenheit. The converse is false; a counterexample is a day that is not 80° Fahrenheit and not sunny.
If it is 80° Fahrenheit, then it is sunny; The converse is false; a counterexample is a day that is 80° and cloudy.
Question 8
(Multiple Choice Worth 1 Points)
(01.05 MC)
Premise 1: All geckos are lizards.
Premise 2: All lizards are reptiles.
Which of the following is a valid conclusion for the two premises?
Therefore, all reptiles are lizards.
Therefore, all lizards are geckos.
Therefore, all geckos are reptiles.
Therefore, all reptiles are geckos.
Question 9
(Multiple Choice Worth 1 Points)
(01.05 MC)
Which statement is logically equivalent to the following conditional statement?
"If it has exactly four sides, then it is not a hexagon."
If it does not have exactly four sides, then it is not a hexagon.
If it does not have exactly four sides, then it is a hexagon.
If it is a hexagon, then it does not have exactly four sides.
If it is not a hexagon, then it has exactly four sides.
Question 10
(Multiple Choice Worth 1 Points)
(01.05 MC)
Which is a counterexample of the following conditional?
"If a number is divisible by seven, then it is odd."
28
21
7
1
(Multiple Choice Worth 1 Points)
(01.05 MC)
What is the biconditional statement of the following conditional statement?
"If a polygon has six sides, then it is a hexagon."
If a polygon does not have six sides, then it is a not hexagon.
A polygon has six sides if and only if it is a hexagon.
If a polygon is a hexagon, then it has six sides.
If a polygon is not a hexagon, then it is does not have six sides.
Question 2
(Multiple Choice Worth 1 Points)
(01.05 MC)
What is the converse of the following statement?
"If the sum of the interior angles of a polygon is 180°, then the polygon is a triangle."
If the polygon is a triangle, then the sum of the interior angles of the polygon is 180°.
If the polygon is not a triangle, then the sum of interior angles of the polygon is not 180°.
If the sum of the interior angles of a polygon is not 180°, then the polygon is not a triangle.
If the sum of the interior angles of a polygon is 180°, then the triangle is a polygon.
Question 3
(Multiple Choice Worth 1 Points)
(01.05 LC)
What is the contrapositive of the following statement?
"If there is rain, then the dog will not bark."
If the dog will bark, then there is no rain.
If there is no rain, then the dog will not bark.
If the dog will not bark, then there is rain.
If there is no rain, then the dog will bark.
Question 4
(Multiple Choice Worth 1 Points)
(01.05 LC)
What is the inverse of the following statement?
"If a polygon does not have five sides, then the polygon is a rectangle."
If the polygon is a rectangle, then the polygon does not have five sides.
If the polygon is not a rectangle, then the polygon has five sides.
If the polygon does not have five sides, then the polygon is not a rectangle.
If the polygon has five sides, then the polygon is not a rectangle.
Question 5
(Multiple Choice Worth 1 Points)
(01.05 MC)
Jenni wrote a conditional statement and its converse.
Conditional: If angles are right angles, then the angles have the same measure.
Converse: If angles have the same measurement, then they are right angles.
Did Jenni write the converse statement properly? Determine if the converse is true or false and give a counterexample if the converse is false.
No; two angles that each measure 45°
Yes; two angles that each measure 90°
Yes; two angles that each measure 41°
No; two angles that each measure 82°
Question 6
(Multiple Choice Worth 1 Points)
(01.05 MC)
Read the following statements.
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg writes, "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."
Cassandra writes, "Statement 2 is the converse of statement 1 and inverse of statement 3."
Who is correct?
Both Meg and Cassandra are incorrect.
Only Meg is correct.
Both Meg and Cassandra are correct.
Only Cassandra is correct.
Question 7
(Multiple Choice Worth 1 Points)
(01.05 MC)
What is the converse of the following conditional statement?
"If it is sunny, then it is 80° Fahrenheit."
Determine if the converse is true or false and give a counterexample if the converse is false.
If it is sunny, then it is 80° Fahrenheit. The converse is true.
If it is 80° Fahrenheit, then it is sunny. The converse is true.
If it is not sunny, then it is not 80° Fahrenheit. The converse is false; a counterexample is a day that is not 80° Fahrenheit and not sunny.
If it is 80° Fahrenheit, then it is sunny; The converse is false; a counterexample is a day that is 80° and cloudy.
Question 8
(Multiple Choice Worth 1 Points)
(01.05 MC)
Premise 1: All geckos are lizards.
Premise 2: All lizards are reptiles.
Which of the following is a valid conclusion for the two premises?
Therefore, all reptiles are lizards.
Therefore, all lizards are geckos.
Therefore, all geckos are reptiles.
Therefore, all reptiles are geckos.
Question 9
(Multiple Choice Worth 1 Points)
(01.05 MC)
Which statement is logically equivalent to the following conditional statement?
"If it has exactly four sides, then it is not a hexagon."
If it does not have exactly four sides, then it is not a hexagon.
If it does not have exactly four sides, then it is a hexagon.
If it is a hexagon, then it does not have exactly four sides.
If it is not a hexagon, then it has exactly four sides.
Question 10
(Multiple Choice Worth 1 Points)
(01.05 MC)
Which is a counterexample of the following conditional?
"If a number is divisible by seven, then it is odd."
28
21
7
1
Answers
GPT-4o mini
Here are the answers to your questions:
**Question 1:** The biconditional statement of the conditional "If a polygon has six sides, then it is a hexagon" is:
- **A polygon has six sides if and only if it is a hexagon.**
**Question 2:** The converse of "If the sum of the interior angles of a polygon is 180°, then the polygon is a triangle" is:
- **If the polygon is a triangle, then the sum of the interior angles of the polygon is 180°.**
**Question 3:** The contrapositive of "If there is rain, then the dog will not bark" is:
- **If the dog will bark, then there is no rain.**
**Question 4:** The inverse of "If a polygon does not have five sides, then the polygon is a rectangle" is:
- **If the polygon is not a rectangle, then the polygon has five sides.**
**Question 5:** Did Jenni write the converse statement properly? Determine if the converse is true or false:
- **No; two angles that each measure 45°.**
**Question 6:** Analyzing the statements, who is correct?
- **Both Meg and Cassandra are incorrect.** (Meg's statement about Statement 3 being the contrapositive is incorrect; Cassandra's statement is also incorrect.)
**Question 7:** The converse of "If it is sunny, then it is 80° Fahrenheit" is:
- **If it is 80° Fahrenheit, then it is sunny; The converse is false; a counterexample is a day that is 80° and cloudy.**
**Question 8:** Based on the premises, a valid conclusion is:
- **Therefore, all geckos are reptiles.**
**Question 9:** The statement logically equivalent to "If it has exactly four sides, then it is not a hexagon" is:
- **If it is a hexagon, then it does not have exactly four sides.**
**Question 10:** The counterexample of "If a number is divisible by seven, then it is odd" is:
- **28** (since 28 is divisible by 7 and is even).
Feel free to ask if you have more questions!
**Question 1:** The biconditional statement of the conditional "If a polygon has six sides, then it is a hexagon" is:
- **A polygon has six sides if and only if it is a hexagon.**
**Question 2:** The converse of "If the sum of the interior angles of a polygon is 180°, then the polygon is a triangle" is:
- **If the polygon is a triangle, then the sum of the interior angles of the polygon is 180°.**
**Question 3:** The contrapositive of "If there is rain, then the dog will not bark" is:
- **If the dog will bark, then there is no rain.**
**Question 4:** The inverse of "If a polygon does not have five sides, then the polygon is a rectangle" is:
- **If the polygon is not a rectangle, then the polygon has five sides.**
**Question 5:** Did Jenni write the converse statement properly? Determine if the converse is true or false:
- **No; two angles that each measure 45°.**
**Question 6:** Analyzing the statements, who is correct?
- **Both Meg and Cassandra are incorrect.** (Meg's statement about Statement 3 being the contrapositive is incorrect; Cassandra's statement is also incorrect.)
**Question 7:** The converse of "If it is sunny, then it is 80° Fahrenheit" is:
- **If it is 80° Fahrenheit, then it is sunny; The converse is false; a counterexample is a day that is 80° and cloudy.**
**Question 8:** Based on the premises, a valid conclusion is:
- **Therefore, all geckos are reptiles.**
**Question 9:** The statement logically equivalent to "If it has exactly four sides, then it is not a hexagon" is:
- **If it is a hexagon, then it does not have exactly four sides.**
**Question 10:** The counterexample of "If a number is divisible by seven, then it is odd" is:
- **28** (since 28 is divisible by 7 and is even).
Feel free to ask if you have more questions!