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Post a LessonAnswered on 25/12/2021 Learn CBSE/Class 12/Mathematics/Unit I: Relations and Functions
Shikha Yadav
Success in CBSE / ICSE Class 12 and 10 Mathematics Boards
Answered on 01 Mar Learn CBSE/Class 12/Mathematics/Unit I: Relations and Functions
Kalaiselvi
Online Mathematics tutor with 4 years experience(Online Classes for 10th to 12th)
Answered on 01 Mar Learn CBSE/Class 12/Mathematics/Unit I: Relations and Functions
Kalaiselvi
Online Mathematics tutor with 4 years experience(Online Classes for 10th to 12th)
The relation which equals the product of the sets on which it is defined is called trivial relation.
1) A relation R in a set A is called empty relation, if no element of A is related to any element of A, i.e., R = CAXA.
2) A relation R in a set A is called universal relation, if each element of A
is related to every element of A, i.e., R = A x A.
So both relations are trivial relation as they are equal to product of A on which they are defined.
read lessAnswered on 06 Apr Learn CBSE/Class 12/Mathematics/Unit I: Relations and Functions
Sadika
A bijective function, also known as a bijection, is a type of function between two sets, where each element in the domain (input) set is paired with exactly one element in the codomain (output) set, and vice versa. In other words, a bijective function establishes a one-to-one correspondence between the elements of the domain and the elements of the codomain.
Formally, a function f:A→Bf:A→B is bijective if and only if:
In simpler terms, a bijective function is both injective (or one-to-one) and surjective (or onto). It means that each element in the codomain is paired with exactly one element in the domain, and there are no "extra" elements left in either set without a corresponding match in the other set.
Graphically, a bijective function can be represented by a plot where each input value has a unique corresponding output value, and there are no horizontal or vertical line tests that intersect the graph at more than one point.
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