Question

elements auu
3.
If A= {a,b,c,d) and R={(a, b)(b,c)}
then
minimum elements add in R so that it would be
symmetric
how
1
D​

Answer 1

Step-by-step explanation:

For R to be equivalence relation, it should be reflexive, symmetric and transitive

Now, R is reflexive

⇒(x,x)ϵR for all xϵ{1,2,3}

⇒(1,1),(2,2),(3,3)ϵR

R is symmetric

⇒(1,2),(2,3)ϵR

⇒(2,1),(3,2)ϵR

R is transitive

⇒(1,2),(2,3)ϵR

⇒(1,3)ϵR

Also (3,1)ϵR as R is symmetric.

So, the total number of elements is 9.

Hence, minimum 7 elements must be added.

hope this can help you