WorksheetsGeometry -- Logic Test Review
Total questions: 27
Worksheet time: 2hrs 15mins
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.
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.
The statement "an angle is a right angle if and only if its measure is 90o" is an example of what type of statement?
Conditional
Conjecture
Biconditional
Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.
Inductive
Deductive
Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.
Inductive
Deductive
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.
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.
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...
If this wind keeps up, then we will lose some trees.
We lost some trees.
Conclusion: The wind kept up!
Invalid
Valid - Detachment
Valid - Syllogism
If a person is a librarian, then they read books.
If a person is a friend of Dana, then they read books.
Therefore, if a person is a librarian, they are a friend of Dana.
Not Valid
Valid, using the Law of Detachment
Valid, using the Law of Syllogism
Which is a valid conclusion given the statement below:
If you go to the store, you will spend money. Joe goes to the store.
Joe goes to a fancy grocery store.
Joe spends money.
He spends less than $100.
Joe and his sister go to the store.
Joe and his sister spend money
Which of the following represents the given statement in symbolic notation, given that p represents "Kate is taking geometry" and q represents "Kate takes an SOL test."
If Kate does not take geometry, then she does not take an SOL test.
q→∼p
p ∧ q
∼p ∨ ∼q
∼p → ∼q
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.
If a mineral has a hardness of 2, it can be scratched with a fingernail.
Using the Law of Syllogism, what logically comes next?
If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
If the length of a side of a square is 5 ft, then the area is 25 ft2.
Determine whether the stated conclusion is valid.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
Invalid
Valid
More information Required
Unknown
If you are at least 25 year old, then you can rent a car.
You can rent a car
If we see John on Monday, then we can ask him over for lunch. We see John on Monday.
John may eat with us.
John saw us on Monday
No conclusion can be made since the hypothesis did not occur.
We asked John to have lunch with us.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
