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PROPOSITIONAL
                                             03                            LOGIC, HARDWARE



                                                                           IMPLEMENTATION,

                                                                    ARITHMETIC OPERATIONS













                      Learning Objectives


                  3.1  Propositional Logic                          3.2  Well-Formed Formulas and Truth Values
                  3.3  Connectives                                  3.4  Converse, Inverse and Contrapositive
                  3.5  Equivalence Propositional Laws               3.6  Tautology, Contradiction and Contingency
                  3.7  Logic Gates                                  3.8  Half Adder and Full Adder



              Logic is the subject that deals with valid reasoning leading to inference. According to Aristotle, “logic is new and
              necessary reasoning”. It is said 'new' because it lets us know the unknown and ‘necessary’ as it leads to important
              conclusions. Logical reasoning is the fundamental base of some branches of Mathematics and Computer Science. Logic
              may be informal, formal, symbolic or mathematical.

              Symbolic logic represents logical expressions by using symbols or variables instead of using language statements.
              Logical expressions are the statements that can either be true or false. An interrogative statement like “Why are plants
              green?” or an imperative statement like “Do your homework” or an exclamatory statement like “What a shot!”, are
              not logical statements. But a declarative statement like “Rohan is the best goalkeeper” can either be true or false or
              in other words, it has a truth value. The statements that produce only true or false as answers are called propositions.
              They are the building blocks of logic.

              Let us examine some statements:

                                        Statements                                   Type
                         The month of May is very hot.            It is a proposition as the answer can be true or false.
                                                                  [mostly true]
                         Disha hates vegetables.                  It is a proposition because the answer can be yes or
                                                                  no.
                         Good morning!                            It is not a proposition as commands or wishes cannot
                                                                  be true or false.
                         What are you reading?                    It is not a proposition as such questions cannot be
                                                                  true or false.


                  3.1 PROPOSITIONAL LOGIC
              Propositional logic is a branch of symbolic logic that deals with propositions and how each proposition relates to
              one another. It studies the ways of joining or changing propositions to form more complex propositions. A proposition
              is represented by propositional variables containing a single letter generally written in lowercase.


                7070  Touchpad Computer Science-XI
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