# 2.3 Relations

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Vad är ett set? vad betyder aEA fast där E är en mer konstig symbol Vad behövs för att två set ska lika? Whn can we say that set A is a sub set of set B and how do we denote that with symbols? Is the empty set a sub set of all sets? Yes What is the cardinality of a set and how do we denote that? What is a powers set? How do we denote that? What is the power set of {a,b,c}?  What is the difference of a set and a collection? The elements in a set are not ordered but in a collection they are. When are two collections equal? When they contain the same elements in the same order. What are 2-tuples called and when are they considers equal? They are called ordered pairs and (a,b) and (c,d) are only equal when a=c & b=d What is to formula to see how many elements a power set has? 2^(nr of original set elements) What is the cartesian product of two sets? It is the resulting ordered collection that you get after combining two sets. What is the cretesian product of the sets {1,2,3} and {a,b,c} What is the union of two sets and how do we denote that?  What are two disjoint sets? they have no elements in common. What is the compliment of a set?  What is the union of a collection of a set? It is the set that contains all elements in all of the collections included in the union What is the intersection of a set? What is a binary relation? it is a set that combines elements of others sets into pairs. Give an example of a binary relation between two real world examples. When pair (a,b) belongs to relation set R how we we describe the relation between a and b? We simply say a is related to b How can we describe the function f from A to B using orderd pairs? We can say that (a,f(a)) When is a relation called reflexive? a binary relation R over a set X is reflexive if every element of X is related to itself. Formally, this may be written ∀x ∈ X : x R x. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. What is difference between identity and reflexive relation? What is the difference between an identity relation and a reflexive relation? ... For example, suppose A={1,2,3}, then the set of ordered pairs {(1,1), (2,2), (3,3)} is the identity relation on set 'A'. Any relation 'R' on a set 'A' is said to be reflexive if (a,a) belongs to 'R', for every 'a' belongs to set 'A'. When a relation transitive? In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b and b is related to an element c then a is also related to c. Transitivity (or transitiveness) is a key property of both partial order relations and equivalence relations.  When is a set Symmetric? Let A be a set in which the relation R defined. Then R issaid to be a symmetric relation, if (a, b) ∈ R ⇒ (b, a) ∈ R, that is, aRb ⇒ bRa forall (a, b) ∈ R.  What is the composite of a function?  All you do is find an element that is in a pair of both sets and combine the elements of both pairs into a new pair. So 1,1 and 1,6 has 1 in common and then you combine the other 1 from R and the 6 from S into 1,6 in the composite pair set. .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorccc ID343069 Card Set2.3 Relations Descriptionentill Updated2018-10-20T11:20:37Z Show Answers