Logic Terms and Concepts, Quizzes of Discrete Mathematics

Download Logic Terms and Concepts and more Quizzes Discrete Mathematics in PDF only on Docsity! TERM 1 Statement DEFINITION 1 A statement is a sentence that is either true or false. Opinions and ambiguous sentences (mathematical or otherwise) are not statements. x+y = 13 this can either be true or false and is not definitely one or the other so it is not a statement. TERM 2 ~ DEFINITION 2 Means not. so ~p is the negation of p TERM 3 V DEFINITION 3 Means or but this "or" implies it can be p or q or both in p V q TERM 4 xor DEFINITION 4 Represented by a circle with a cross in it. This is also "or" but it means an exclusive or. in p xor q it means p or q but not both. TERM 5 ^ DEFINITION 5 This means "and" it represents the situation where you have p and q TERM 6 Logically equivalent DEFINITION 6 To be logically equivalent means to have identical truth values in a truth table TERM 7 Tautology DEFINITION 7 A tautology means a statement that is always true. Represented by a bold t. TERM 8 Contradiction DEFINITION 8 A statement that is always false; represented by a bold "c". TERM 9 If-Then Statements DEFINITION 9 A conditional statement with a hypothesis that leads to a conclusion. If the hypothesis is p and the conclusion q this statement is represented by p --> q TERM 10 p --> q equivalence DEFINITION 10 p -- >q = ~p V q TERM 21 Argument DEFINITION 21 a sequence of statements called premises which lead to a final statement, the conclusion. For an Argument to be valid, when all of the premises are true the conclusion is always true. This is best shown in a truth table. TERM 22 Premise DEFINITION 22 A premise is a condition given in an argument which leads to a conclusion. In truth tables for arguments the conclusion is only considered if all premises are true! TERM 23 Modus Ponens DEFINITION 23 Major Premise : p --> qMinor Premise: p is trueTherefore q is true TERM 24 Modus Tollens DEFINITION 24 Major Premise: p --> qMinor Premise: ~ qConclusion : ~p TERM 25 Generalization DEFINITION 25 Premise: PConclusion: P V Q TERM 26 Specialization DEFINITION 26 Premise: P ^ QConclusion: P TERM 27 Elimination DEFINITION 27 Major Premise: P V QMinor Premise: ~PConclusion: Q TERM 28 Transitivity DEFINITION 28 Major Premise: p --> qMinor Premise: q --> rConclusion: p --> r TERM 29 Ways to prove Argument validity DEFINITION 29 Truth Tables, and Table of Logical Equivalence lawsmainly: DeMorgan's Laws, Distributive laws, Associative Laws,and Commutative LawsThe rest you need to know but not by name, see the other set of flashcards for more description of these lawsAlso Venn Diagrams TERM 30 Predicate DEFINITION 30 A sentence with a finite number of values, which becomes a statement when the values are substituted for a variable TERM 31 Domain DEFINITION 31 The set of all values that can be substituted into a predicate TERM 32 Truth Set DEFINITION 32 A set of all values in a domain where the predicate is true.If given a polynomial with variables solve the polynomial using quadratic equation to show how the truth set was found. TERM 33 Quantifiers DEFINITION 33 Universal and Existential A word that shows the quantity of possible values for a variable in a statement. TERM 34 Universal Quantifier DEFINITION 34 Key Words:for all, every, each, any, arbitrary, each, given any TERM 35 Z DEFINITION 35 This is for Integers a + or - can define it for positive or negative integers only