Deductive Reasoning

What does deductive reasoning use to form its arguments?

• patterns

• specific cases

• observed examples

• facts, definitions, accepted properties, and laws of logic

How would you describe the Law of Detachment symbolically?

• if p -> q is true and q is true; then p is true

• if p -> q is true and p is true; then q is true

• if p -> q and q -> r, then p -> r

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If you passed the final, then you pass the class. You passed the final.

• You passed the class.

• You didn't pass the class

• Not possible

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If your parents let you borrow the car, then you will go to the movies with your friend. You will go to the movies with your friend.

• Your parents let you borrow the car.

• Your parents didn't let you borrow the car.

• Not possible

Tags

CCSS.HSS.CP.A.5

How would you describe the Law of Syllogism symbolically?

• if p -> q is true and q is true, then p is true.

• if p -> q is true and p is true, then q is true.

• if p -> q is true and q -> r is true, then p -> r is true

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.

If x < -2, the |x| > 2. If x > 2, then |x| > 2.

• If x < -2, then x > 2.

• If |x| > 2, then x > 2.

• Not possible

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.

If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure is a quadrilateral.

• If a figure is a rhombus, then the figure is a quadrilateral.

• If a figure is a quadrilateral, then the figure is a rhombus.

• Not possible

Which law of logic is illustrated by these statements?

If you miss practice the day before a game, then you will not be a starting player in the game.

You miss practice on Tuesday. You will not start the game Wednesday.

• Law of Detachment

• Law of Syllogism

• Speed Limit

• None of the above

Which law of logic is illustrated by the following statements?

If <1 and <2 are vertical angles, then <1 is congruent to <2. If <1 is congruent to <2, then m<1 = m<2.

If <1 and <2 are vertical angles, then m<1 = m<2.

• Law of Detachment

• Law of Syllogism

• 5th Amendment

• Not possible

Tags

CCSS.HSG.CO.C.9

If the school cafeteria sells pizza today, Greg is going to eat four pieces. Pizza is on sale for school lunch today.

Using deductive reasoning, what statement can you make based on this information?

• Lots of people will buy pizza.

• The school cafeteria sells pizza.

• Greg will eat four pieces of pizza.

• Greg needs to go on a diet.