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What is an antichain?
An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable.
What are the first numbers in an ordered pair?
They are the elements from the first set in the original Carestian product. For example, if you make ordered pairs on an x-y plane, then they are the elements of the set X.
A set of two elements in which the order is specified?
It is called an ordered pair.
What is the meaning of AxB as applied to set theory?
it denotes the set of ordered pairs with elements of A and b in the format (a,b)
What is the Formula for the number of subsets in a set?
If the set has n elements, the number of subsets (the power set) has 2n members.
What is an antichain?
An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable.
State the principal of duality in boolean algebra?
If {X,R} is a Partially Ordered Set, then {X,R(inverse)} is also a Partially Ordered Set.
What are the first numbers in an ordered pair?
They are the elements from the first set in the original Carestian product. For example, if you make ordered pairs on an x-y plane, then they are the elements of the set X.
What are the set of ordered pairs for y equals 0.1 x plus 1?
They are elements of the infinite set of ordered pairs of the form (x, 0.1x+1). It is an infinite set and I am not stupid enough to try to list its elements!
What does join mean in maths?
A join and meet are binary operations on the elements of a POSET, or partially ordered set. A join on a set is defined as the supremum with respect to a partial order on the set, provided it exists. A meet on a set is defined either as the unique infimum with respect to the partial order imposed on the set, if the infimum exists.
A set of two elements in which the order is specified?
It is called an ordered pair.
What is the set of the first numbers of the ordered pairs in a relation called?
they are the first set of paired elements
Why duplicate tuples are not allowed in DBMS?
Since relation is a set, and tuples are element of a set, according to set theory, the elements of a set are not ordered.
What is the meaning of AxB as applied to set theory?
it denotes the set of ordered pairs with elements of A and b in the format (a,b)
What is a poset?
It is a partially ordered set. That means it is a set with the following properties: a binary relation that is 1. reflexive 2. antisymmetric 3. transitive a totally ordered set has totality which means for every a and b in the set, a< or equal to b or b< or equal to a. Not the case in a poset. So a partial order does NOT have totality.
What is the middle number of an ordered set of numbers?
If there is an odd number of elements in the set, then it is the median. If there is an even number, then there is no middle number.
What is the Formula for the number of subsets in a set?
If the set has n elements, the number of subsets (the power set) has 2n members.
