Show Tautology without Truth Table

In this class, We discuss Show Tautology without Truth Table.

The reader should have prior knowledge of the list of equivalence formulas. Click here.

Example 1:

Show that (p ∧ q) -> (p ∨ q) is a tautology.

We need to reduce the given proposition to true.

We use the equivalence formulas from our previous class.

Idea: ( p ∨ ¬p) = T

We need to reduce the proposition by ( p ∨ ¬p).

The below diagram shows the output.

Example 2:

Show that the given proposition is a tautology.

((p ∨ q) ∧ ¬(¬p ∧ (¬q ∨ ¬r))) ∨ (¬p ∧ ¬q) ∨ (¬p ∧ ¬r))

The below diagram shows the output.