Therefore: how modus ponens works
You know P → Q. You know P. ∴ Q. Every deduction in every puzzle is built from steps like this one.
How it works
An argument is a list of premises followed by a conclusion. The symbol ∴ means therefore. It marks the line you are allowed to write down because of the lines above it.
The most basic step is modus ponens. If you know P → Q and you know P, you know Q. The conditional is a promise, P makes it come due, and Q is what it promised.
An argument is valid when the conclusion is true in every world where all the premises are true. Validity is about the form, not the board in front of you. A valid argument with a false premise can still end in a false conclusion.
Worth memorizing
From P → Q and P, conclude Q.
This is modus ponens, the most used step in logic.
∴ means “therefore”.
It marks a line that follows from the lines above it.
Valid means the conclusion can’t be false while every premise is true.
A valid argument with a false premise promises nothing.
Practice
0 of 5 rightPremises: Tet(b) → Large(b). Tet(b). Which conclusion follows?
Premises: Small(c) → LeftOf(c, a). Small(c). Which conclusion follows?
An argument is valid, and its conclusion is false. What do you know?