Argument patterns

Question 1

Conjunction

Answer 1

conjunction is a statement if the form

P and Q

“I am running, and it’s sunny”

made up of two conjuncts

Question 2

disjunction

Answer 2

Any statement P or Q

“Either the movie night was cancelled or my friends said they were going to show up”

made up of disjuncts

Question 3

Negation

Answer 3

Not P

~P

It is NOT sunny

Question 4

Conditional

Answer 4

if P, then Q

‘If it rains, the picnic will be cancelled”

“if jones committed the murder, the butler is sad”

If my friends don’t show up to movie night will be cancelled

Question 5

Biconditional

Answer 5

A biconditional is a statement if the from

P if and only Q

You can enter the club if only if you have Id

Question 6

Argument by Elimination

Answer 6

1. P or Q
2. ~P
3. Q (from 1,2)

Either the bus comes or I have to walk home

the bus did not come

Therefore, I walked home

Question 7

False argument by elimination?

Answer 7

1. P or Q
2. you assert P
3. Q

Looks similar, but invalid

Either the bus comes or I have to walk home

I walked home

therefore, the bus didn’t come (this is invalid)

Question 8

Conjunction

Answer 8

1. P
2. Q
3. p and Q (from 1,2)

Joe is working out and eating at the same time

joe is eating

Question 9

Affirming the Antecedent

Answer 9

1. if P, then Q
2. P
3. Q (from 1,2)
   If P is true, then Q has to be true

if I’m going to the movies then I will buy popcorn
I went to movies
therefore, I bought popcorn

Question 10

Denying the consequent

Answer 10

1. If P then Q
2. ~Q
3. ~P (from 1,2)

If jack goes to Egypt then he will visit the pyramids

Jack did not visit the pyramids

therefore Jack did not go to Egypt

Question 11

If I’m hungry then I will eat
I didn’t eat
therefore I am not hungry

is an example of

Answer 11

Denying the Antecedent

1. If P, then Q
2. ~P
3. ~Q

THIS IS INVALID

Question 12

If I smoke weed, then my eyes will be red
my eyes are red
therefore, I smoked weed

This is an example of ?

Answer 12

Affirming the Consequent

1. If P, then Q
2. Q
3. P

THIS IS INVALID

Question 13

What does Hypothetical syllogism look like?

Answer 13

1. If P, then Q
2. If Q, then R
3. If P then R (from1,2)

If I commit a crime then I will go to jail

If I go to jail then I won’t be able to see family

therefore, if I commit a crime I won’t be able to see family

Question 14

Contraposition

Answer 14

1. If P, then Q
2. If ~Q
3. then ~P (from1)

If I commit a crime then I will go to jail

if I don’t commit a crime,

then I won’t go to jail

Question 15

Universal Modus Ponens

Answer 15

1. All A’s are B’s
2. x is an A
3. x is B

Example:

All new TTC buses have wifi inside

This is a new TTC bus

Therefore, this TTC bus has wifi installed

Question 16

Universal Modus Tollens

Answer 16

1. All A’s are B’s
2. x is not B
3. x is not A

All new new phones are fast

The Iphone 2 is not fast

therefore, the Iphone 2 is not a new phone

Question 17

Universal Hypothetical Syllogism

Answer 17

1. All A’s are B’s
2. All B’s are C’s
3. All A’s are C’s

All pizza’s are made with dough

Anything made with dough has water

therefore, All pizza’s have water

Question 18

Universal Ruling out

Answer 18

1. No A’s are B’s
2. x is an A**
3. x is not a B

No cars can fly

Tesla is car

therefore, Tesla’s can’t fly

Question 19

All dogs are mean

Jim is not a dog

therefore, Jim is not mean

an example of….

Answer 19

1. All A’s are B’s
2. x is not A

INVALID

Question 20

All dogs are mean

Hercules is mean

therefore, Hercules is a dog.

is an example of..

Answer 20

All A’s are B’s

x is a B

x is not an A

INVALID