Table of Contents
What does ordered triple mean?
In general, a solution of a system in three variables is an ordered triple (x, y, z) that makes ALL THREE equations true. In other words, it is what they all three have in common. So if an ordered triple is a solution to one equation, but not another, then it is NOT a solution to the system.
What can you say about the ordered pairs AB and BA?
The pair of elements that occur in particular order and are enclosed in brackets are called a set of ordered pairs. If ‘a’ and ‘b’ are two elements, then the two different pairs are (a, b); (b, a) and (a, b); (b, a). In an ordered pair (a, b), a is called the first component and b is called the second component.
What does ∩ mean in set theory?
The set A ∩ B—read “A intersection B” or “the intersection of A and B”—is defined as the set composed of all elements that belong to both A and B. Thus, the intersection of the two committees in the foregoing example is the set consisting of Blanshard and Hixon.
Is a set of ordered pairs in which no two ordered pairs that have the same first component?
Function. A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range.
What is C in set theory?
In set theory, the complement of a set A, often denoted by Ac (or A′), are the elements not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U that are not in A.
What are ordordered triples?
Ordered triples are defined recursivley, so that ( x, y) = { { x }, { x, y } } and ( x, y, z) = ( ( x, y), z). Observe that ( ( x, y), z) only has two elements, ( x, y) and z, so we can just apply the definition.
What is the ordered pair of a A and B?
Also, for any a a and b b, the pair {a,b} { a, b } is the same as the pair {b,a} { b, a }. So, if we wish to take into account the order in which the two elements of a pair are given, we need to find another way of representing the pair. Thus, we define the ordered pair (a,b) (a, b) as the set {{a},{a,b}} { { a }, { a, b } }.
What is the basic relation in set theory?
The basic relation in set theory is that of elementhood, or membership. We write a ∈A a ∈ A to indicate that the object a a is an element, or a member, of the set A A. We also say that a a belongs to A A. Thus, a set A A is equal to a set B B if and only if for every a a, a ∈ A a ∈ A if and only if a ∈ B a ∈ B.
How do you prove two sets are equal?
Thus, two sets are equal if and only if they have exactly the same elements. The basic relation in set theory is that of elementhood, or membership. We write \\(a\\in A\\) to indicate that the object \\(a\\) is an element, or a member, of the set \\(A\\).