PPT-Logical Equivalence of Propositions

Dr Yasir Ali Two statement forms are called logically equivalent if and only if they have identical truth values for each possible substitution of statements for their statement variables. 1. Tautologies, Contradictions, and Contingencies. A . tautology. is a proposition that is always . true. .. Example: . p. . ∨¬. p. . A . contradiction. is a proposition that is always . false. From Aaron Bloomfield... Used by Dr. . Kotamarti. 2. Tautology and Contradiction. A tautology is a statement that is always true. p .  ¬p will always be true (Negation Law). A contradiction is a statement that is always false. Recap. Common . Three-Way Equivalence:. Sentence . meanings. The objects of the attitudes. The referents of ‘that’-. clauses. We can call whatever is all of these things a “proposition.” Now we have the question: what are propositions?. Peter M. Maurer. Propositions. A proposition is a declarative sentence that can be either true or false. Earth is a planet – True. The Moon is made of green cheese – False. There is life on Mars – We don’t know yet, but either there is or there isn’t. Introduction and . Scope. Propositions. Fall 2011. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . supporting . What is an Argument?. Based on 2 statements with a 3. rd. that follows the first two. . One major premise. One minor premise. Conclusion . Premise: statement used as evidence for a conclusion. Conclusion: statement that is supported by at least one premise. Seminal work: Language, Truth and Logic. This was published when he was 26. . He was the most outspoken proponent of Logical Positivism.. Attended Eton and was fairly precocious.. Scholarship to Christ Church, Oxford to study classics.. Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . Semantics Unit 2 Part 2. A Sentence. A grammatically complete series of words that expresses a complete thought.. S + V + expresses a complete thought. I would like a cup of coffee . is a sentence. . The assertion at the end of the sequence is called the . conclusion. , and the preceding statements are called . premises. . . To have confidence in the conclusion that you draw from an argument, you must be sure that the premises are acceptable on their own merits or follow from other statements that are known to be true.. Mrs. Skaff. Symbol. In Words. Meaning. p, q, . or. r. ¬. . Symbol. In Words. Meaning. p, q, . or. r. ¬. What is Logic?. Logic is a way to describe situations or knowledge that enables us to reason from existing knowledge to new conclusions. . – 1.5. Chapter 1 (Logic). . Propositions and logical operations (1.1). Evaluating compound propositions (1.2). Conditional statements (1.3). Logical equivalence (1.4). Laws of propositional logic (1.5). Prepositionals. Suppose there are two compound statements, X and Y, which will be known as logical equivalence if and only if the truth table of both of them contains the same truth values in their columns. With the help of symbol = or ⇔, we can...