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Logic, Sets, and Proofs - Amherst College

Logic, Sets, and ProofsDavid A. Cox and Catherine C. McGeochAmherst College1 LogicLogical statementis a mathematical statement that is eithertrue or false. Here we denote logical statements with capital lettersA, B. Logicalstatements be combined to form new logical statements as follows:NameNotationConjunctionAandBDisj unctionAorBNegationnotA AImplicationAimpliesBifA, thenBA BEquivalenceAif and only ifBA BHere are some examples of conjunction, disjunction and negation:x >1 andx <3: This is true whenxis in the open interval (1,3).x >1 orx <3: This is true for all real numbersx. (x >1): This is the same asx are two logical statements that are true:x >4 x > 1 (x= 1 orx= 1).Note that x= 1 orx= 1 is usually writtenx= , Contrapositives, and begin with converses andcontrapositives: Theconverseof AimpliesB is BimpliesA.

Logic, Sets, and Proofs David A. Cox and Catherine C. McGeoch Amherst College 1 Logic Logical Statements. A logical statement is a mathematical statement that is either true or false. Here we denote logical statements with capital letters A;B. Logical statements be combined to form new logical statements as follows:

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