Showing Valid Inference Examples 2

In this class, We discuss Showing Valid Inference Examples 2.

The reader should have prior knowledge of Showing Valid Inference Examples 1. Click here.

Example 1:

Show that (s ∨ r) is tautologically implied by (p ∨ q) ∧ (p -> r) ∧ (q -> s)

The above question can be asked in another way.

Show that (s ∨ r) is a valid inference from the given premises (p ∨ q), (p -> r), (q -> s)

Solution:

The below diagram shows the derivation.

Example 2:

Show that r ∧ (p ∨ q) is a valid inference from the premises (p ∨ q), (q -> r), (p -> m), ¬m

Solution:

The diagram below shows the derivation