##### C.T- EXAM 1

Modus Ponens

What's the symbol?

Is it valid or invalid? Why or Why not?

If P,then Q

P

∴ Q

This is Valid

Modus Tollens

What's the symbol?

Is it valid or invalid? Why or Why not?

If P, then Q

~Q

∴ ~P

Hypothetical Syllogism

What's the symbol?

Is it valid or invalid? Why or Why not?

If P,then Q

If Q, then R

So,if P, then R

Disjunctive Syllogism

What's the symbol?

Is it valid or invalid? Why or Why not?

P v Q

~P

∴Q

Valid

Affirming the Consequent

What's the symbol?

Is it valid or invalid? Why or Why not?

If P, then Q

Q

∴ P

Invalid

Denying the Antecedent

What's the symbol?

Is it valid or invalid? Why or Why not?

If P,then Q

~ P

∴ ~ Q

Invalid

Tautology

Definition

Symbol

Example

A Tautology is Necessarily True. It is and empty statement, void of content

A v ~ A

Either someone in here has a cold or no one in here has a cold.

Contradiction

Definition

Symbol

Example

A Contradiction is Necessarily False. It is not Possible

A . ~ A

Someone in here has a cold, and no one in here has a cold.

Contingent

Definition

Symbol

Example

A Contingent's truth value is determined by reality/states of affairs/facts

A.

Someone in here has a cold

Give an example of Modus Ponens

If it rains, then the ground will be wet

It's raining

So the ground is wet

Give an example of Modus Tollens

If it rains, then the ground is wet

The ground isn't wet

So it's not raining

Give an example of Hypothetical Syllogism

If I sell my car, then I'll get $1,500

If I get $1,500 then I can go to Spain in July

So if I sell my car, then I can go to Spain in July

Give an example of Disjunctive Syllogism

He will either buy a Honda or Toyota

He won't buy a Honda

So he'll buy a Toyota

Give an example of Affirming the Consquent

If Larry's first record solo sold a million copies, he'll be rich

Larry's rich

So, his first record solo sold a million copies

(He could have won the lottery, sold a million copies of his second solo, inherited the money)

Give an example of Denying the Antecedent

If Larry's first record solo sold a million copies,he'll be rich.

His first record didn't sell a million copies

So, he's not rich

(Larry could have sold a million on his second record, or hit the lottery, or inherited some $$$)

Deductive Argument

Definition

Example

An argument may be taken as deductive if the turth of its premises is intended to guarantee the truth of its conclusion

All humans are mortal

Sally is a human

∴ Sally is mortal

Inductive Argument

Definition

Example

An argument may be taken as inductive if the truth of its premises is intended to make likely/probably but not guarantee the truth of its conclusion

Every lawyer that I have met has been agressive

Since you blind date tonight is a lawyer, she will probably be aggressive.

Name 3 possibilites for an argument to be valid?

1) All true premises and true conclusion

2)All on some false premises and true conclusion

3)All on some false premises and false conclusion

Give an example of a valid argument displaying this: All true premises and true conclusions

All humans are mammals

The author of this book is a human

So,the author is a mammal

Give an example of a valid argument displaying this: All on some false premises and true conclusion

All reptiles are mammals

The author of this book is a reptile

So, the author is a mammal

Give an example of a valid argument displaying this: All on some false premises and false conclusion

All frogs wear pink boots

Jimmy Carter was a frog

So Jimmy Carter wore pink boots