Functions and Relations

Question

What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ?

 

Thanks.

Answer 1

|A| = m and |B| = n , then
No. of functions from A to B = n^m

So total no of functions =4^4

but we have condition x=y so

then total no of functions =4      F= {(0,0),(1,1),(2,2),(3,3)}

Total no of relation on given function F=2^n

Total no of relation on given function F=2^4=16

Comments

I also thought the same answer as yours, but the answer given was 16. :(

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Sorry little bit mistake I will correct now.

I thought you were asking no of function but you are asking for no of relations

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https://www.geeksforgeeks.org/last-minute-notes-engineering-mathematics/

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I think number of reflexive relation should be 2^12. Please correct me if I am wrong