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Definition

                      A proposition is a declarative statement which can either be true or false, but not both or any other value.




                 2.1.1 Types of Proposition
                 A proposition is of two types which are as follows:
                 •  Simple proposition: It contains a single atomic statement. Some examples of simple propositions are:
                   1. “Java is an object-oriented programming language.”
                   2. “The earth revolves around the sun.”
                 •  Compound  proposition: It contains two or more simple propositions joined by special symbols called
                   connectives.
                   Some examples of compound propositions are:
                   1. “Java is an object-oriented programming language and Java is platform-independent.”
                   2. “He is playing the piano or he is playing the flute.”

                 In the first example, the connective “and” is used, and the connective “or” is used in the second example.

                     2.2 WELL-FORMED FORMULAS AND TRUTH VALUES
                 Well-formed formulas (WFF) is the representation of propositional logic in the form of symbols or abbreviations. It is a
                 statement that can either be true or false. Thus, all simple propositions are well-formed formulas. For example,

                 A: Java is an object-oriented programming language.
                 B: Java is platform-independent.

                 In the above example, both statements are represented by symbols, i.e., A and B. Hence, it is a well-formed formula.
                 Any propositional statement formed by using A and B, then (A ∧ B), (A ∨ B), (A → B), etc. are well-formed formulas.


                 2.2.1 Truth Value and Truth Table
                 The truth or falsity of a proposition is called its truth value. A simple proposition can either be true or false. The truth
                 value of a compound proposition is calculated from the truth values of its components using certain logical rules.
                 A compound proposition is truth-functional which means it accepts truth values as input and produces a unique truth
                 value as output.
                 The logical process of finding conclusions from given propositions is known as syllogism and the propositions used to
                 draw conclusions are called the premises.

                 A proposition is generally expressed and evaluated with the help of a truth table. The truth table is a table containing
                 all possible combinations of inputs and their corresponding outputs listed in tabular form. Truth values in a truth
                 table are denoted either by T and F or by 0 and 1. A logic circuit’s truth table with n binary inputs will have 2ⁿ input
                 combinations or rows. For example, the truth table of disjunction is given below.

                                                       a            b          a ∨ b

                                                       0            0            0
                                                       0            1            1
                                                       1            0            1

                                                       1            1            1




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