Chapter 2 Test Review

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Terms in this set (54)
logically equivalent statementstwo statements are this if, and only if, (iff) they have the same truth values in every possible situation. Uses triple equal signDe Morgan's Laws for Logicshow that ~ (p ^ q) triple equals ~p v ~qconditional statementa statement that can be written in if-then form (implications)Euler Diagramdetermines the validity of arguments in which hypotheses contain the words all, some, and no (none) circle diagramssetany collection of objectselementindividual objects in a setwell-defined setif we are given a set and some particular object, then we must be able to tell whether the object does or does not belong to the setdescribing a setcan use listing, or roster method, or set-builder notationequal setstwo sets are ____ if, and only if, they contain exactly the same elementsone-to-one correspondenceUsed to compare two sets in which one element matches one and only on element in the other set.equivalent setstwo sets A and B are ____, written A ~ B, if, and only if, there exists a one-to-one correspondence between the setscardinal numbersindicates the number of elements in the set, denoted n(S) =empty set ( 0 with slash or { } )a set that contains no elements has a cardinal number 0, and is auniversal set (U)the set that contains all elements being considered in a given discussioncomplement of a set (A with line over it)the set of all elements in a given universal set U that are not in Asubsets ( B c line under, A)B is a ___ of A, if, and only if, every element of B is an element of A2^nhow to determine the number of subsets in a setproper subset (B c A)every element of B is an element of A, and there is at least one element of A that is not an element of B2^n - 1how to determine a proper subsetset intersection (n)the set of all elements common to both A and Bunion set (u)the set of all elements in A or in Bset difference (B - A)the set of all elements in B that are not in ACartesian Product (A x B)the set of all ordered pairs such that the first component of each pair is an element of A and the second component of each pair is an element of Bpis a statement~ pis the negation of p (statement) which means not pVor^andiffif and only ifp -> qimplication statementq -> pimplication converse~p -> ~qimplication inverse~q -> ~pimplication contrapositivecontrapositivethe contrapositive of the ____ is the original statementbiconditionala statement that contains the words "if and only if"set theoryGreg Cantor createdlisting methodc = {1,2,3,4}set builder notationc = { x I x E N and x < 5}Fundamental Counting PrincipleIf event M can occur in m ways and event N can occur in n ways, then event M followed by event N can occur in m • n waysequivalentif two sets, A and B, are ____, then A and B have the same cardinal number; n(A) = n(B)finite seta set when the cardinal number of the set is zero or a natural number, can count thisinfinite setcannot be counted, the set N of natural numbers is thisemptythe ___ set is a subset of every setdisjoint setsif sets A and B have no elements in common they areset differencethe complement of A relative to B, written A-B, is the set of all elements in B that are not in A