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                                                                         BOOLEAN ALGEBRA

















                        Learning Objectives

                    1.1  Propositional Logic                        1.2  Truth Values
                    1.3  Symbols or Connectives                     1.4  Well-Formed Formulas, Premises and Syllogism
                    1.5  Converse, Inverse and Contrapositive       1.6  Precedence of the Connectives
                    1.7  Equivalence Propositional Laws             1.8  Tautology, Contradiction and Contingency
                    1.9  Boolean Algebra                            1.10  Maxterm, Minterm, Sum of Product and Product of Sum
                    1.11  Derivation of a Boolean Expression from Multiple Logical Statements
                    1.12  Introduction to Karnaugh Maps             1.13  Formation of Groups by Overlapping
                    1.14  Grouping by Map Rolling                   1.15  Redundant Groups



                 Logic is the subject that deals with valid reasoning leading to inference. Logical reasoning is the fundamental base of
                 some branches of Mathematics and Computer Science. Logic may be informal, formal, symbolic, or mathematical.
                 Symbolic logic is the logic used to represent logical expressions by using symbols or variables instead of language
                 statements. Logical expressions are statements that can either be ‘True’ or ‘False’. However, interrogative statements
                 like “Why the sky is blue?”, or imperative statements like “Finish your work first”, or exclamatory sentences like “What
                 a beautiful dress!”, do not come under the category of logical statements, as these are not answered in ‘True’ or
                 ‘False’. Meanwhile, declarative statements like “Gajendra is the best bowler.”, or “New Delhi is the capital of India.”
                 can be called logical statements, as these statements can either be ‘True’ or ‘False’; or in other words, they have a
                 truth value. Such types of statements that produce only true or false as answers are thus called propositions and these
                 propositions are the building blocks of logical reasoning.
                 Let us examine some statements.

                                          Statement                                       Type
                        The month of January is very cold.            It is a proposition as the answer can be true or false
                                                                      [mostly true].
                        Misha likes fruits.                           It is a proposition because the answer can be yes or no.
                        Good afternoon!                               It is not a proposition as commands or wishes cannot
                                                                      be true or false.
                        What are you eating?                          It is not a proposition as such questions cannot be true
                                                                      or false.



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                                                                                                      Boolean Algebra   13
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