Q. 9 B4.2( 6 Votes )

If A = {1, 2, 3, 4}, define relations on A which have properties of being

symmetric but neither reflexive nor transitive.

Answer :

Recall that for any binary relation R on set A. We have,


R is reflexive if for all x A, xRx.


R is symmetric if for all x, y A, if xRy, then yRx.


R is transitive if for all x, y, z A, if xRy and yRz, then xRz.


Using these properties, we can define R on A.


A = {1, 2, 3, 4}


We need to define a relation (say, R) which is symmetric but neither reflexive nor transitive.


The relation R must be defined on A.


Symmetric relation:


R = {(1, 2), (2, 1)}


Note that, the relation R here is neither reflexive nor transitive, and it is the shortest relation that can be form.


Similarly, we can also write:


R = {(1, 3), (3, 1)}


Or R = {(3, 4), (4, 3)}


Or R = {(2, 3), (3, 2), (1, 4), (4, 1)}


And so on…


All of these are right answers.


Thus, we have got the relation which is symmetric but neither reflexive nor transitive.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 01Functions - 01Functions - 0152 mins
Range of FunctionsRange of FunctionsRange of Functions58 mins
Quick Revision of Types of RelationsQuick Revision of Types of RelationsQuick Revision of Types of Relations59 mins
Some standard real functionsSome standard real functionsSome standard real functions61 mins
Battle of Graphs | various functions & their GraphsBattle of Graphs | various functions & their GraphsBattle of Graphs | various functions & their Graphs48 mins
Functions - 09Functions - 09Functions - 0947 mins
Quick Recap lecture of important graphs & functionsQuick Recap lecture of important graphs & functionsQuick Recap lecture of important graphs & functions58 mins
Range of Quadratic/quadratic & linear/Linear functionsRange of Quadratic/quadratic & linear/Linear functionsRange of Quadratic/quadratic & linear/Linear functions45 mins
Understand Fractional part and Mod Function in 1 hourUnderstand Fractional part and Mod Function in 1 hourUnderstand Fractional part and Mod Function in 1 hour61 mins
Functions - 06Functions - 06Functions - 0648 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