Question

Give an example of each compounds that pq and r can may represent

Answer 1

Tautology/Contradiction/Contingency.

Definition 2.1.1. A tautology is a proposition that is always true.

Example 2.1.1. p ∨ ¬p

Definition 2.1.2. A contradiction is a proposition that is always false.

Example 2.1.2. p ∧ ¬p

Definition 2.1.3. A contingency is a proposition that is neither a tautology

nor a contradiction.

Example 2.1.3. p ∨ q → ¬r

Discussion

One of the important techniques used in proving theorems is to replace, or substitute, one proposition by another one that is equivalent to it. In this section we will

list some of the basic propositional equivalences and show how they can be used to

prove other equivalences.