Question 1(Multiple Choice Worth 1 points)
(01.05 MC)
Which is a counterexample of the following conditional?
"If a number is divisible by five, then it is even."
30
25
20
18
Question 2(Multiple Choice Worth 1 points)
(01.05 LC)
What is the inverse of the following statement?
"If a shape has four sides, then it is not a triangle."
If a shape has four sides, then it is a triangle.
If a shape is not a triangle, then it has four sides.
If a shape does not have four sides, then it is a triangle.
If a shape is a triangle, then it does not have four sides.
Question 3(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 4(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 5(Multiple Choice Worth 1 points)
(01.05 MC)
Which statement is logically equivalent to the following conditional statement?
"If it has exactly five sides, then it is not an octagon."
If it is not an octagon, then it has exactly five sides.
If it does not have exactly five sides, then it is not an octagon.
If it does not have exactly five sides, then it is an octagon.
If it is an octagon, then it does not have exactly five sides.
Question 6(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 7(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 8(Multiple Choice Worth 1 points)
(01.05 MC)
Premise 1: All lions are cats.
Premise 2: All cats are mammals.
Which of the following is a valid conclusion for the two premises?
Therefore, all mammals are lions.
Therefore, all mammals are cats.
Therefore, all cats are lions.
Therefore, all lions are mammals.
Question 9(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 10(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 1: 25
Question 2: If a shape is not a triangle, then it does not have four sides.
Question 3: If the polygon is a triangle, then the sum of the interior angles of the polygon is 180°.
Question 4: If the dog will bark, then there is no rain.
Question 5: If it does not have exactly five sides, then it is an octagon.
Question 6: If it is 80° Fahrenheit, then it is sunny. The converse is false; a counterexample is a day that is 80° and cloudy.
Question 7: No; two angles that each measure 45°
Question 8: Therefore, all mammals are cats.
Question 9: Only Meg is correct.
Question 10: A polygon has six sides if and only if it is a hexagon.