Exam 2

Question 1

Modus Ponens

P > Q
P
•Q

Answer 1

If A then B.
A is true.
Then B is also true

If you buy the popcorn, then you’ll need a drink.
You bought the popcorn
So you need a drink

Question 2

Modus Tollens

P>Q
~Q
•~P

Answer 2

If P then Q
Not P
Therefore not Q

If you get the candy, you won’t need the popcorn
She needed popcorn
So she didn’t get the candy

Question 3

Hypothetical Syllogism

P>Q
Q>R
•P>R

Answer 3

If P then Q
If Q then R
So if P then R

If you sing while driving you’ll be more attentive

If your more attentive your a good driver

Therefore, if you sing while driving, your a good driver

Question 4

Disjunctive Syllogism

P v Q
~P
•Q

Answer 4

Either A or B
A is not the case
So, B is the case

Either Jade will get rid of his bike or he’ll fix it
She didn’t fix his bike
So he got rid of it

Question 5

Conjuction

P
Q
•P*Q

Answer 5

P is true, Q is also true
So both P and Q are true

Ice is tricky to walk on
Mud sticks to your shoes
So, ice is tricky to walk on and mud sticks to your shoes

Question 6

Simplification

P*Q
•P

Answer 6

P and Q are true
So A or B is true

She likes both skiing and jazz
Therefore, she likes skiing

Question 7

Addition

P
•P v Q

Answer 7

P is true
Therefore, either A or B

She drove in the blizzard
Therefore, she found it hard to drive in the blizzard or was kidding about how she got the dent

Question 8

Constructive dilemma

P>Q
R>S
P v R
•Q v S

Answer 8

If P then Q, and, if then S then R
Either P or Q
Therefore, either C or D

If I eat the popcorn, I’ll feel guilty, but if I eat the carrots, I’ll want popcorn.
Either I eat the popcorn or eat the carrots.
Therefore either I feel guilty or I want the popcorn.

Question 9

Destructive dilemma

P>Q
R>S
~Q v ~S
•~P v ~R

Answer 9

If P then Q, and, if R then S.
Either not Q or not S.
Therefore, either not P or not C

If I was the pretzel, I’ll need a drink, but I I eat ice cream, I’ll want the choco
Therefore, either I didn’t eat the pretzel or I didn’t eat the ice cream