This chapter illustrates how Logic and Mathematics are specialized specialized linguistic structures. Mathematics is the language of science and technology. The logic assists us in deciding the validity of the arguments. The truth and falsity of the arguments are directly validated by mathematical theory. This chapter explains the concepts of different types of propositions, truth tables, connectives, inferences, properties, and quantifiers through the brainstorming activities or experiments. This chapter explains truth tables and various logical operations such as Conjunction, Disjunction, Conditional and biconditional statements through an innovative approach to the operations of set theory. This analogy enhances the understanding of the concepts and their applications in different ways. Furthermore, it elucidates the concepts of tautology and contradiction with suitable examples. It also helps to improve the mathematical and logical thinking of the readers through the concepts of Algebra of Propositions, quantifiers and its applications. Furthermore, this chapter explores the hypothesis of the concepts of conditional and biconditional statements. The chapter concludes with case studies and exercises aimed at connecting theoretical relational structures to real-world applications across various disciplines.