The Theory of Propositional Logics in Reference of Boolean Algebra

Abstract

In this article, we will prove that set of complex numbers C = a + ib, where a, b ∈ R and i = imaginary number also known as by iota (i = √-1), is the set of largest number, whereas the set of natural numbers N = {1, 2, 3, …, n, …} is the set of least numbers through logical approach of validity of argument using logic of Boolean algebra and through different algebraic operations. We shall verify through rule of detachment by applying them on identity relation N ⊂ W ⊂ I ⊂ Q ⊂ R ⊂ C or C ⊃ R ⊃ Q ⊃ I ⊃ W ⊃ N. It will be proved by using Boolean algebra table and different Boolean algebraic properties.