Logical Reasoning

Underline the hypothesis and italicize the conclusion in each statement.

• If your dog eats Purina, then he’ll stay happy and healthy.

• If your dog eats Purina, then he’ll stay happy and healthy.

• If your dog eats Purina, then he’ll stay happy and healthy.

• If your dog eats Purina, then he’ll stay happy and healthy.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• If a polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

• If the polygon is not a quadrilateral, then it is not a trapezoid.

• If the polygon is not a trapezoid, then it is not a quadrilateral.

• If the polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Tags

CCSS.HSG.CO.A.1

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is a counterexample of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

Tags

CCSS.HSG.CO.A.1

The statement "an angle is a right angle if and only if its measure is 90^o" is an example of what type of statement?

• Conditional

• Conjecture

• Biconditional

Tags

CCSS.HSG.CO.A.1

Using the Law of Detachment, draw a conclusion based on the statements given:

If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.

• Sarah will get stuck in the security line.

• Sarah will have a long flight.

• Sarah will need to bring a neck pillow and headphones.

• Sarah will get stuck with a middle seat on the plane.

Tags

CCSS.HSS.CP.A.5

Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.

If you study, then you will pass the test. If you pass the test, then you will pass the class.

• If you study, then you will pass the class.

• If you pass the test, then you should study.

• If you pass the class, then you will pass the test.

• If you study, then you will pass the test.

Given:  If I get an A on my test then my mom will buy me a TV.
I got a 94 on my test.
what conclusion can be made.

• I am smart.
• I got an A on my test.
• My mom will buy me a TV.
• I must have cheated.

Tags

CCSS.RI.8.1

CCSS.RI.9-10.1

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

What is the hypothesis of the following statement: "If Johnny is late to school, then his mom will have to drive him."

• His mom will have to drive him
• If Johnny is late to school
• Johnny is late to school
• Then his mom will have to drive him