Deductive Reasoning

Deductive Reasoning

Law of Syllogism

Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement.

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What can you conclude from the given information?

If a figure is a square, then the figure is a rectangle.

If a figure is a rectangle, then the figure has four sides.

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What can you conclude from the given information?

If a whole number ends in 0, then it is divisible by 10.

If a whole number is divisible by 10, then it is divisible by 5.

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What can you conclude from the given information?

If a river is more than 4000 miles long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 miles long.

Multiple Choice

What does deductive reasoning use to form its arguments?

• patterns

• specific cases

• observed examples

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

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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.

Multiple Choice

What can you conclude from the given true statements?

If an animal is a dog, then they like biscuits.

Sammy is a dog.

• Sammy is a Great Dane

• Sammy likes biscuits.

• We can't conclude anything.

• Sammy is really a cat.

Multiple Choice

What can you conclude from the given true statements?

If you live in Orlando, then you live in Florida.

You live in Orlando

• You don't live in Florida.

• You hate snow.

• You live in Florida

• We can't conclude anything.

Multiple Choice

What can you conclude from the following true statements.

If I study for one hour each day, then I will score well on the exam.

I score well on the exam.

• I studied for one hour each day.

• I studied a lot.

• I didn't study.

• We can't conclude anything.

Multiple Choice

What can you conclude from the following true statements?

If you do gymnastics, then you are flexible.

If you do ballet, then you are flexible.

• If you play dance, then you are flexible.

• You are flexible.

• Nothing!