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
