Unit 1: Logic

What is a counterexample of the statement below?

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

• Duck

• Penguin

• Rabbit

• Snake

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

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.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

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

Let p represent: Two angles are supplementary.

Let q represent: The angles have a sum of 180°

What is the symbolic representation of the following statement;

If two angles have a sum of 180°, then the angles are supplementary.

• p -> q

• ~p -> q

• q -> p

• ~q -> ~p

Tags

CCSS.8.G.A.5

Which of the following biconditional statements is true?

• Today is Friday if and only if yesterday was Thursday.

• You live in the state of Arizona if and only if you live in the United States.

• You live in the United States if and only if you live in North America.

• Today is Saturday if and only if tomorrow is Monday.

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.

Original: If angles are congruent, then the measures of the angles are equal.

What is this? If angles are not congruent, then the measures of the angles are not equal.

• Conditional

• Converse

• Inverse

• Converse

Tags

CCSS.8.G.A.2

What word(s) is associated with a conditional statement?

• and

• or

• If, then

• if and only if

Tags

CCSS.RL.11-12.9

CCSS.RL.6.3

CCSS.RL.7.3

CCSS.RL.8.3

CCSS.RL.9-10.3