Week 2 Flashcards
what are 2 important features of a sequence
. Order does matter
(1,2,3) , (1,3,2) are different
.Repeated occurences matter
(H,E,L,L,O) , (H,H,H,E,L,L,O), (H,E,L,O) all different
What is a tuple
a finite sequences
What does the k in k tuple represent
the length of the tuple
What does it mean when two tuples are equal
. They have the same length
. Corresponding elements are the same
What is an ordered pair
A two tuple
What is a cartesian products of sets ( eg of A and B )
All the ordered pairs (x,y) where x exists in a and y exists in B
What is a relation of A to B
A subset of the cartesian product (A x B)
What are the 2 ways to represent a relation
. directed graph
. 0 -1 matrix
What is important to look out for in a 0-1 matrix
The order horizontally is the same as the order vertically
What does it mean by reflexive
. every element has a loop
.(a,a) exists in R for every element a where a exists in A
What are examples of reflexive relations
<= , >= , = , divisibility
What does irreflexive mean
.There are no loops at all
. ( a,a ) does not exist in R for evey element a that exists in set A
what are examples of irreflexive relations
<, > , not equal to
symmetric
when a,b exist in A
If (a,b) exists in relation so does (b,a)
. all arrows are reversible
antisymmetric
if (a,b) exists in R (b,a) cannot exist in R unless a =b ( a loop)
. arrows are not reversible unless it is a loop
