Lecture 2.4 - Deductive Reasoning

Match

For the conditional:

"If you are a wildcat, then you are spicy."

Match the following statements.

• If you are spicy, then you are a wildcat.

• If you are not a wildcat, then you are not spicy.

• If you are not spicy, then you are not a wildcat."

• You are a wildcat if and only if you are spicy.

converse

inverse

contrapositive

biconditional

• converse

• inverse

• contrapositive

• biconditional

​2.4 - Deductive Reasoning

Let's use some facts, homie.

​Deductive Reasoning

→​ uses facts, rules, definitions, or properties to reach conclusions from given statements​

Multiple Choice

The type of reasoning where a person makes  conclusions based on observations and patterns is called...

• Inductive reasoning
• Deductive reasoning
• Conjecture
• Experiments

Multiple Choice

A type of reasoning that uses general facts, definitions, and accepted properties in a logical order to write a logical argument.

• Inductive

• Deductive

• Logic

• Reasoning

Multiple Choice

All bears are mammals, all mammals have kidneys; therefore all bears have kidneys. 

• Deductive
• Inductive

Multiple Choice

Obtuse angles are greater than 90 degrees.  This angle is 110 degrees, so it is obtuse. 

• Deductive
• Inductive

Multiple Choice

All observed houses on South Street have roofs that are falling apart.  Sherry lives on South Street.  Her roof is falling apart. 

• Deductive
• Inductive

Multiple Choice

You see the numbers 2, 4, .... and decide the next number must be a 6

What type of reasoning was used?

• Inductive

• Deductive

Multiple Choice

Since all humans are mortal, and I am human, then I am mortal. 

• Deductive
• Inductive

Multiple Choice

All chickens that we have seen have been brown; so, all chickens are brown. 

• Deductive
• Inductive

Multiple Choice

It is dangerous to drive on icy streets.  The streets are icy now so it is dangerous to drive now. 

• Deductive
• Inductive

Multiple Choice

I saw the light on and the tea kettle is hot on the stove. Someone must be home.

• Deductive

• Inductive

​Law of Detachment

Multiple Choice

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If two lines do not intersect, then they are coplanar and parallel, or skew.

Premise: Lines AB and CD do not intersect.

• Lines AB and CD are parallel and not coplanar.

• Lines AB and CD are skew.

• Lines AB and CD are parallel and coplanar or they are skew.

• No Conclusion can be made.

Multiple Choice

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If there is lightening, then it is not safe to out in the open.

Premise: Mary sees lightening from her home

• It is not safe for the lightening.

• It is not safe for Marty to be out in the open.

• There is lightening.

• No conclusion can be made.

Multiple Choice

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If points lie on a line, then they are collinear.

Premise: Points X, Y, and Z are in line m.

• They are not collinear.

• They are collinear.

• They are points.

• No conclusion can be made.

Multiple Choice

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If n is an even number, then it is divisible by 2.

Premise: 4834 is an even number.

• 4834 is an integer.

• 4834 is divisible by 2.

• 4834 is not divisible by 2.

• not possible

Multiple Choice

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

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

Premise: I will score well on the exam.

• I study for 1 hour each day.

• I do not study for 1 hour each day.

• If I do well on the exam, I studied for 1 hour each day.

• not possible

​Law of Syllogism

Multiple Choice

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

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.

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

• If a whole number ends in 0, then it is divisible by 5.

• Not possible

Multiple Choice

If it continue to rain, then the track and field oval will become wet and slippery.

If the track and field oval will become wet and slippery, then the track and field game will be cancelled.

• If it continue to rain, then the track and field game will be cancelled.

• If he track and field game will be cancelled., then it continue to rain.

• Not possible

Multiple Choice

If you are resting, then you will be relaxed.

If your heartbeat is normal, then you are relaxed.

• If you are resting, then your heartbeat is normal.

• If your heartbeat is normal, then you are resting.

• Not possible

Multiple Choice

Statement 1: If you exercise regularly, then you have a healthy body

Statement 2: If you have a healthy body, then you have more energy

• You have more energy

• If you exercise regularly, then you have more energy

• You have a healthy body

• If you do not have a healthy body, then you do not exercise regularly

Multiple Choice

Statement 1: If the sun is shining, it is a beautiful day.

Statement 2: If it is a beautiful day, then we will go hiking.

• If the sun is not shining, we will not go hiking.

• If we go hiking, then it is a beautiful day.

• If the sun is shining then we will go hiking.

• No conclusion can be made.

Multiple Choice

Statement 1: If you go to the swimming pool, then you enjoy yourself.

Statement 2: If you enjoy yourself, then you will want to return.

• If you return to the pool you will enjoy yourself.

• If you enjoy yourself, then you went to the pool.

• If you go to the pool, you will want to return.

• No conclusion can be made.

TWO conditionals are true which makes FIRST hypothesis and SECOND conclusion true in form of a conditional. Looks like the transitive property.

Syllogism

ONE conditional and ONE hypothesis associated to that conditional is true

Detachment

​What's the difference?

What is life though, bro?

Multiple Choice

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Multiple Choice

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Multiple Choice

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• None

Multiple Choice

(1) If you have a can opener, you can open a can.
(2) Jon has a can opener.
(3) John can open a can.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Syllogism
• Law of Detachment
• invalid

Multiple Choice

(1)  If it is a rabbit, then it has long ears.
(2)  Peter Cottontail has long ears.
(3)  Peter Cottontail is a rabbit.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• invalid

Multiple Choice

Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.

• Law of Detachment
• Law of Contrapositive
• Law of Syllogism
• Law of Biconditional

Multiple Choice

Which law of logic is this:
If my mom stays home, then she won't buy shoes.
If she doesn't buy shoes, then she'll wear an old pair. 
Therefore if my mom stays home, then she will wear an old pair of shoes.

• Contrapositive
• Converse
• Detachmant
• Syllogism