Set Theory - Question 1 0.0 / 5 ? MathematicsSet Theory and General TopologyUniversityNone Created by: Lara_BryceCreated on: 18-04-19 20:50 What happens if two columns are equal? The relation is true. 1 of 20 What does ~P mean? Not P. 2 of 20 What does contradiction mean? Never true. 3 of 20 What does tautology mean? Always true. 4 of 20 What does P => Q mean? If P then Q. 5 of 20 What is the truth table of P => Q? Always true, apart from P=T and Q=F. 6 of 20 What is P necessary for Q, in symbols? Q => P. 7 of 20 What is P sufficient for Q, in symbols? P => Q. 8 of 20 Draw the OR gate. Triangle, from two lines to one. 9 of 20 Draw the AND gate. Curve, from two lines to one. 10 of 20 Draw the NOT gate. Triangle, one line throughout. 11 of 20 What is Zorn's Lemma? Let X be a non-empty partially ordered set in which every totally ordered subset has an upper bound. Then X contains at least one maximal element. 12 of 20 What is a shortened version of Zorn's Lemma? X non-empty, partially ordered set, every totally ordered subset has upper bound. X has a max. 13 of 20 What is Zorn's Lemma the same as? The axiom of choice and the well-ordered principle. 14 of 20 What conditions are needed for an equivalence relation? Reflexive, Symmetric, Transitive. 15 of 20 What does reflexive mean? For every a e A, <a,a> e R. 16 of 20 What does symmetric mean? If <a,b> e R, then <b,a> e R. 17 of 20 What does transitive mean? If <a,b> e R and <b,c> e R, then <a,c> e R. 18 of 20 If R is an equivalence relation in A, then the equivalence class of any element a e A... Denoted [a], is the set of elements to which a is related by [a] = {x : <a,x> e R}. 19 of 20 What are De Morgan's Laws? Complement swaps union and intersection; eg. (AUB)c = Ac ^ Bc. 20 of 20
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