Question

How many relation are there on n to n ? I don't get what it means while I know its result .

Comments

you mean set of natural numbers N to N , or a set of n elements to another set of n elements?

Answer 1

Relation are defined on element of same set so for a set of n element we will take cross product to map each relation thus we our relationship can have n*n element

Eg S={1,2} to {1,2} so Relations={(1,1),(1,2),(2,1),(2,2}

Now out of $n^{2}$ relations each relation have option to either be present or absent thus

$2^{n^{2}}$ total

Like only 1 relation is present so (1,1) or (1,2) or (2,1) or (2,2) if 2 are present like {(1,2),(2,2)} etc

In other ways it is equivalent to number of different n*n matrix possible where each entry can be 0 or 1

Comments

Not getting bro

Plz clarify these lines...

Like only 1 relation is present so (1,1) or (1,2) or (2,1) or (2,2) if 2 are present like {(1,2),(2,2)} etc
In other ways it is equivalent to number of different n*n matrix possible where each entry can be 0 or 1

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Out of {(1,1),(1,2),(2,1),(2,2)} we have to define relation

So relation of 1 cardinality can be either of (1,1) (2,2) (3,3) (4,4)

Similarly for 2 Cardinality you will have 6 different combinations possible

For 4 Cardinality you will have everything {(1,1),(1,2),(2,1),(2,2)}