Law of Contrapositive, Detachment, and Syllogism

Which of the following is logically equivalent to the statement,

“ If a mouse can drive a car, then a pigeon can do algebra.”

• If a pigeon can drive a car, then a mouse can do algebra.

• If a mouse can't drive a car, then a pigeon can't do algebra.

• If a pigeon can't do algebra, then a mouse can't drive a car.

• If a mouse can't do algebra, then a pigeon can't drive a car.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

According to the law of ___, the conditional and the contrapositive are either BOTH true or BOTH false.

• contrapositive

• conditional

• truth

• syllogism

Which of these is the law of detachment?

• p → q

  p

  ∴ q

• p → q

  q → r

  ∴p → r

• p → q

• p → q T

  ∴ ~q → ~p T

Which of these is the law of syllogism?

• p → q

  p

  ∴ q

• p → q

  q → r

  ∴p → r

• p → q

• p → q T

  ∴ ~q → ~p T

Which of the following is logical conclusion to the statement,

"If Ryan wears plaid pants, then he will have a good day. Ryan wore yellow plaid pants."

• Ryan has a great fashion sense.

• Ryan likes the color yellow.

• Yellow plaid is proven in studies to increase happiness.

• Ryan will have a good day.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Which of the following is logically conclusion for to the statement,

"If memorize the formulas, then I will know them for the test. If I know the formulas on the test, then I will get an A+."

• Formulas are important.

• I am not going to get an A+, because I do not know the formulas.

• If I memorize the formulas, then I will get an A+.

• What formulas?

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Consider the following,

"If a shape is a square then it is a parallelogram. If a shape is a parallelogram, then opposite sides are congruent."

Which of these is a logical conclusion?

• If a shape is a square, then it is also a rhombus.

• If a shape is a square, then it has opposite sides that are congruent.

• If a shape is a parallelogram, then is is not a triangle.

• All parallelograms are cool.

Tags

CCSS.HSG.CO.C.11

Consider the statement,

"If Maxine is hungry, then she will eat anything even anchovies. Maxine is hungry."

Which of the following is a logical conclusion.

• Maxine isn't very hungry.

• Maxine will eat anchovies

• Maxine won't eat anchovies

• Maxine isn't that hungry.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Consider the statement,

"If there is a fire, then the fire department will receive a call."

Which of these statements is logically equivalent?

• If the fire department does not receive a call, then there is not fire.

• If there is no fire, then the fire department will not receive a call.

• If there is a fire department, then they put out fires.

• If the fire department receives a call, then there is a fire.

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A