Q. What is identity relation of sets? explain with example.
Answers
Answer:
An identity relation on a set 'A' is the set of ordered pairs (a,a), where 'a' belongs to set 'A'. 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'.
Answer:
A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation.
A function is a type of relation. But, a relation is allowed to have the object x in the first set to be related to more than one object in the second set. So a relation may not be represented by a function machine, because, given the object x to the input of the machine, the machine couldn't spit out a unique output object that is paired to x.