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CS245 Exam #2
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Terms in this set (28)
Horn Clause
A disjunction of predicate in which at most one of the predicates is not negated
Set
an unordered collection of distinct objects
subset
set A is a ___ of B if all the elements in A can also be found in B
proper subset
A is a ___ of B when A is a subset of B and B does not equal A.
power set
The set of all subset of a set, including the empty set
disjoint
Sets that have no elements in common
partition
separates all members of a set into disjoint subsets
ordered pair
a group of 2 items such that (a, b) != (b, a) unless a = b
Cartesian product
the set of all ordered pairs (a, b) such that a e set A and b e set B
matrix
is an n dimensional collection of values, n in Z+
square matrix
a two dimensional matrix in which the # rows = the # columns
equal (matrix)
two matrices that have the same dimensions and each pair of corresponding elements is equal
transposition
the ___ of a m x n matrix is the n x m matrix where the rows of A are the columns of At
symmetric (matrix)
a matrix A is ___ iff A = At
matrix multiplication
the ___ of an m x n matrix A and an n x o matrix b is an m x o numeric matrix C = A
B in which cij = sum(k=1->n)(aij
bkj)
Identity matrices
are n x n matrices populated with 1 down the main diagonal
nth matrix power
of a square matrix A, denoted An is the result of n-1 successive matrix products of A. A^0 = Im
logical matrix product
for an m x n 0-1 matrix A and an n x o matrix B is an m x o matrix C = A o B in which cij = OR (aik AND bkj)
rth logical matrix power
for an n x n 0 - 1 matrix A (A^[r]) is the n x n matrix resulting from r - 1 successive logical matrix products
(binary) relation
from set X to set Y is a subset of the cartesian product of the domain X and the codomain Y
reflexive
a relation R is ___ on set A if (a, a) e R, for all a e A
symmetric
A relation R is ___ on set A if, whenever (a, b) e R then (b, a) e R for a, b e A.
antisymmetric
A relation R on set A is ___ if, whenever (a,b) e R and a != b then (b, a) !e R, for all a, b e A
transitive
A relation R on set A is ___ if whenever (a, b) e R and (b,c) e R, then (a, c) e R for a, b, c e A.
proof by contraposition
if p then q; assume not q
proof by contradiction
if p then q, assume p and not q
0-1 Join
A or B
0-1 meet
A and B
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