Geometry- Logic & Reasoning Unit 1 Review

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.

If this wind keeps up, then we will lose some trees.

The wind keeps up.

• No valid conclusion possible

• Yes, using the Law of Detachment

• Yes, using the Law of Syllogism

• Yes, using the Law of Contrapositive

What is a counterexample of the statement below?

"If an animal has wings, then it can fly."

• Duck

• Penguin

• Rabbit

• Snake

What is the converse of "If you are hungry, then you did not eat lunch?"

• If you did not eat lunch, then you are hungry.

• If you are not hungry, then you ate lunch.

• If you ate lunch, then you are not hungry.

• You are hungry if and only if you did not eat lunch.

Given: If Amanda goes to the restaurant, then she will order a hamburger.

Given: If she orders a hamburger, then she will get fries.

Conclusion: If Amanda goes to the restaurant, then she will get fries.

• Law of Detachment

• Invalid

• Law of Syllogism

• Law of Contrapositive

Q. 

Which of the following statements is logically equivalent to

"If you live in a mansion, then you have a big heating bill."?

• If you have a big heating bill, then you live in a mansion.

• If you do not have a big heating bill, then you do not live in a mansion.

• If you do not live in a mansion, then you do not have a big heating bill.

• If you live in a mansion, then you do not have a big heating bill.

Given the conditional;

"If Jose eats fish, then he has an allergic reaction"

Which of the following is the symbol representation of " If Jose has an allergic reaction, then he ate fish."

• None of these

• ∼q→∼p

• q→p  

• ∼p→∼q

Tags

CCSS.HSS.CP.A.3

Let p represent; Sam gets a job.

Let q represent; Sam will be available after school.

Which symbolically represents the following argument;

If sam gets a job, then he won't be available after school.

Sam is available after school.

Therefore, Sam did not get a job.

• p-> ~q

  q

  ∴~p

• q-> p

  ~q

  ∧~p

• p-> q

  ~q

  ∴~p

• p-> ~q

  ~q

  ∨~p