Logically Valid Arguments

Question 1

modus ponens

Answer 1

A —> B
A = B
If it rains, I will stay home. It’s raining, therefore I will stay home.

Question 2

Modus Tollens

Answer 2

A —-> B
B does not = A does not
If there is a fire, there is always smoke.
There is no smoke. Therefore, there is no fire.

Question 3

Syllogism

Answer 3

A —-> B
B—-> C
A=C
All men are mortal. Socrates is a man.
Therefore, Socrates is mortal.