ZEAL test-series : Cardinality of relation!

Question

I know that the number of equivalence relation is bell no. i.e 7th bell no. i.e. 877, but i am not able to find the cardinality of R!

Please help!

Comments

in the question given that 3 equivalence classes.

So, we need to divide the given set into 3 partitions.

Here asking the cardinality of R, cardinality of R is a integer. It doesn't have any relation with what are those elements in R.

i mean to say, let R1={(1,2),(1,3)} R2={(5,7),(9,11)} both are different relations but their cardinalities are equal. So, elements are not matters in the partition only no.of elements in a partition is matter.

 

if one partition have n elements, then it contributes n$^2$ elements in the relation. why ? ( think about it )

 

there are 7 elements in set, you need three partitions which make relation R cardinality maximum.

it's same as, 7 vertices, 3 components maximum number of edges possible (be aware of directed graph instead of undirected graph)

 

My intention is not to answer your question, just giving some basic knowledge how to solve your question.

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minimum cardinality of R is 2*2 + 2*2 + 3*3 = 17 , right @Shaik Masthan sir ?

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yes.

Answer 1

Why cant the classes be {1,2,3} {5,7,9} {11} (elements are arbitrarily taken)
This would give a cardinality of : 3*3 + 3*3 +1*1 = 19