Equivalence without Truth Table Examples

In this class, We discuss Equivalence without Truth Table Examples.

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

Example 1:

Show that P -> (q -> r) <=> (p ∧ q) -> r

We need to show LHS is equal to RHS.

We use the equivalence formulas discussed in our previous classes.

The below diagram shows the proof.

Example 2:

Show that (¬p ∧ (¬q ∧ r)) ∨ (q ∧ r) ∨ (p ∧ r) <=> r

The below diagram shows the proof.