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Vad är ett set?
vad betyder aEA fast där E är en mer konstig symbol
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Vad behövs för att två set ska lika?
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Whn can we say that set A is a sub set of set B and how do we denote that with symbols?
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Is the empty set a sub set of all sets?
Yes
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What is the cardinality of a set and how do we denote that?
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What is a powers set?
How do we denote that?
What is the power set of {a,b,c}?
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What is the difference of a set and a collection?
The elements in a set are not ordered but in a collection they are.
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When are two collections equal?
When they contain the same elements in the same order.
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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
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What is to formula to see how many elements a power set has?
2^(nr of original set elements)
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What is the cartesian product of two sets?
It is the resulting ordered collection that you get after combining two sets.
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What is the cretesian product of the sets
{1,2,3} and {a,b,c}
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What is the union of two sets and how do we denote that?
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What are two disjoint sets?
- they have no elements in common.
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What is the compliment of a set?
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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
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What is the intersection of a set?
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What is a binary relation?
- it is a set that combines elements of others sets into pairs.
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Give an example of a binary relation between two real world examples.
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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
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How can we describe the function f from A to B using orderd pairs?
We can say that (a,f(a))
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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.
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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'.
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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.
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When is a set Symmetric?
- Let A be a set in which the relation R defined. Then R is
- said to be a symmetric relation, if (a, b) ∈ R ⇒ (b, a) ∈ R, that is, aRb ⇒ bRa for
- all (a, b) ∈ R.
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What is the composite of a function?
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- 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.
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