Tautology, Contradiction, and Contingency in Propositional Logic

In discrete mathematics, tautology, contradiction, and contingency are important concepts that are used to evaluate the truth or falsity of logical statements. A tautology is a statement that is always true, regardless of the truth values of the propositions it contains. For example, the statement "A or not A" is a tautology because it is true regardless of whether A is true or false. On the other hand, a contradiction is a statement that is always false. For example, the statement "A and not A" is a contradiction because it is impossible for A to be both true and false at the same time. Lastly, a contingency is a statement that is neither a tautology nor a contradiction. It's a statement that is true or false depending on the truth value of the propositions it contains. For example, the statement "If it rains, I will take an umbrella" is a contingency because it is true if it rains, and false otherwise. In this video, we will explore these concepts in more detail, including examples and exercises to help you understand and apply them in your own work. We will also discuss how these concepts are used in the field of logic, including in the evaluation of logical arguments and in the design of digital circuits. Contact Details (You can follow me at) Instagram: https://www.instagram.com/ahmadshoebkhan/ LinkedIn: https://www.linkedin.com/in/ahmad-shoeb-957b6364/ Facebook: https://www.facebook.com/ahmadshoebkhan Watch Complete Playlists: Data Structures: https://www.youtube.com/watch?v=jEMmThJ-1ss&list=PL1QH9gyQXfgsy3G_J33ug6_mWeEBodovC Theory of Computation: https://www.youtube.com/watch?v=p1oqDS0fayc&list=PL1QH9gyQXfgsUBfYUR0WirJASgif4pHVX Compiler Design: https://www.youtube.com/watch?v=XMt-KL-xn7k&list=PL1QH9gyQXfguPNDTsnG90W2kBDQpYLDQr Design and Analysis of Algorithms: https://www.youtube.com/playlist?list=PL1QH9gyQXfgs7foRxIbIH8wmJyDh5QzAm Graph Theory: https://www.youtube.com/watch?v=KB00Ogt36nM&list=PL1QH9gyQXfgvyk6oTWypAi9Yv3G9OQaCX #Tautology #Contradiction #Contingency #DiscreteMathematics #Logic #TruthValues #Propositions #DigitalCircuits #LogicalArguments #TruthTables #BooleanAlgebra #ValidArguments #LogicalFallacies #PropositionalLogic #FormalLogic #DeductiveReasoning #ProvingLogicalStatements #BooleanLogic #PropositionalFormulas #LogicalEquivalence #LogicalEntailment #LogicalReasoning #LogicalConsistency #LogicalImplications #LogicalTruth #LogicalValidity #LogicalInference #LogicalCalculus #LogicalReasoningTechniques #LogicalConsistencyChecking #LogicalProof #LogicalEntailmentChecking #LogicalImplicationChecking #DiscreteMath #LogicTheory #LogicalStatements #FormalReasoning #LogicalConcepts