Understanding Inference Rules

In this class, We discuss Understanding Inference Rules.

The reader should have prior knowledge of tautological implications. Click Here.

We take an example and understand inference rules.

Example:

S1: If it is snowing, then they will not play the match.

S2: It is snowing

The atomic statements from the above statements are

P: It is snowing

Q: They will not play a match

We write S1 as P -> Q

We write S2 as P.

If someone said the above two statements, S1 and S2 are true.

Can we say Q is true?

The two statements P and P -> Q are true.

We write as P ∧ (P -> Q). because both statements are true.

(P ∧ (P -> Q)) -> Q is tautolology.

We say that if (P ∧ (P -> Q)) is true, then Q will be true.