# What is the difference between Modus Ponens and Modus Tollens?

15

Again in the study of mathematical logic, how to differentiate a modus ponens proposition from a modus tollens ?

asked by anonymous 26.06.2016 / 17:20

17

Modus ponens and modus tollens are ways of solving logical implications. A logical implication is a clause in the following form:

And it means:

If p is true, then q is also true.

# Modus ponens

Modus ponens occurs when we have this:

What it means:

If p is true, then q is also true. p is true.

And so, the logical consequence is:

q is true.

And so, modus ponens is defined this way:

p
q   -----
∴ q

# Modus tollens

modus tollens occurs when we have this:

p → q
¬ q

What it means:

If p is true, then q is also true. q is false.

And so, the logical consequence is:

p is false.

The reason for this is because if p is true, then q would also have to be true. But since q is false, then it is not possible that p is true, so p can only be false.

And so, modus tollens is defined as follows:

p → q
¬ q
-----
∴ ¬ p

# Differentiation

So, the main way to differentiate is that:

In modus ponens , you use the implication to prove that the consequence is true in demonstrating that the premise is true .

In
26.06.2016 / 17:38