Solution to Determine whether the following relations are injective and/or subjective function. Find universe of the functions … - Sikademy
Author Image

Archangel Macsika

Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist. i. A= v,w,x,y,z, B=1,2,3,4,5 R= (v,z),(w,1), (x,3),(y,5) ii. A = 1,2,3,4,5 B=1,2,3,4,5 R = (1,2),(2,3),(3,4),(4,5),(5,1)

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Part 1

A=\{v,w,x,y,z\} ; B=\{1,2,3,4,5\}\\ R= (v,z), (w,1), (x,3) (y,5)

R is not a function as a \in A but z \not \in B

So, (v,z) can not be possible for a function

Neither injective nor subjective function and no inverse exists

Part 2

A = \{1,2,3,4,5\}, B=\{1,2,3,4,5\}\\ R = \{(1,2),(2,3),(3,4),(4,5),(5,1)\}

Then as for every a \in A, there is unique b \in B such that (a,b) \in R

\implies R is subjective

The inverse of R exists

R^{-1}= \{(2,1),(3,2),(4,3),(5,4),(1,5)\}

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-1524-qpid-1262