Answer :

Here we are given


X = {1, 2, 3, 4, 5}, Y = { 1, 3, 5, 7, 9 }


(i) R1 = {(x, y)| y = x + 2, x X , y Y }


So using the value we can write the function in set form


R1 = {(1,3),(3,5),(5,7)}


From the above form it’s clear that as the elements of X doesn’t have a unique image in Y so it’s not a function.


(ii) R2 = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}


Here R2 is a function as all the element of X has a distinct image in Y. As 1 and 2 of X is related to 1 of Y and 3, 4 of X is related to 3 of Y so this function is onto function.


(iii) R3 = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}


Here in this relation 1 of X is related to 1 and 3 of Y which clearly contradict the definition of a function which says that every elements of a domain should have at most one image. So it’s clear that it’s not a function.


(iv) R4 = {(1, 3), (2, 5), (4, 7), (5, 9), (3, 1)}


The above expression is a onto and one-one function as all the elements of X has a unique image in Y and no two elements of X have same image in Y. these functions are also termed as bijective function.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Heights and Distances-IHeights and Distances-IHeights and Distances-I45 mins
Sphere and HemisphereSphere and HemisphereSphere and Hemisphere16 mins
Resources and Development RevisionResources and Development RevisionResources and Development Revision28 mins
Cube and CuboidCube and CuboidCube and Cuboid41 mins
History - Concept and QuestionsHistory - Concept and QuestionsHistory - Concept and Questions57 mins
Corrosion: Types, Pros and ConsCorrosion: Types, Pros and ConsCorrosion: Types, Pros and Cons41 mins
Right Circular CylinderRight Circular CylinderRight Circular Cylinder45 mins
Right Circular Cone And FrustumRight Circular Cone And FrustumRight Circular Cone And Frustum43 mins
Revision on Substitution and  Elimination MethodRevision on Substitution and  Elimination MethodRevision on Substitution and Elimination Method44 mins
Area Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and Concepts59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

A function <img sTamil Nadu Board - Math

Let A = { 6, 9, 1Tamil Nadu Board - Math

State whether theTamil Nadu Board - Math

Let A = {5, 6, 7,Tamil Nadu Board - Math

The following tabTamil Nadu Board - Math

Write the pre-imaTamil Nadu Board - Math

Represent the funTamil Nadu Board - Math

A function <img wTamil Nadu Board - Math

Let A = {4, 6, 8,Tamil Nadu Board - Math

For the given funTamil Nadu Board - Math