The collection of perfectly defined objects is a Set. Sets and Relations according to their name bear different properties. Set theory was given by “Georg Cantor”. The collection of definite Numbers is termed as elements of Sets. Letter of alphabet, people, number, etc. can be the elements of Sets. Set ‘A’ and ‘B’ can be equal only if they have same elements. Precisely there are two ways of depicting the element of sets. The first way is by Intentional definition with the use of rule. Suppose set ‘A’ elements has the first four whole numbers.
Set ‘B’ has the color of Japanese flag.
The other way is Extensional definition which is designated with the use of disclosure of the list of elements in curly brackets.
Illustration: A=0, 1, 2, 3,
B = white, red.
The element which a set consists of elements must bear unique characteristics and set operation we are using must have this property. In this way the set relation works.
Now coming to the relations these are not only the things which takes place with the number while set relations work together. To understand the relation properly we must go through its several properties which are shown below:
Reflexive - Suppose you have given the element of set say 'm', whether this relation holds true or not we have to sort out this by putting it at the equal stage and at with the less than type. If the status derived is unclear to you this reflects the property of reflexive nature where it has the unchanged property.
Symmetric - we can easily understand this property with example now by taking the set say of (n, m) which must relate to (m, n), this defines the property of the symmetric relation. We can also say that with the extension of reflexive property we can define the property of symmetric relation.
Transitive – Here also we have to consider the example to explain the transitive property if n = m and m = o then in brief we can also write it as n = o this is the format which explains transitive property.
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Binary Relation...Read More
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