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Trivial Relation

How many triv...

Question

How many trivial relations can be formed on a set which has 64 elements?

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Solution

We saw that trivial relation is either empty relation or universal relation(definition). So the only two trivial relations we can form are empty relation and universal relation.

$\Rightarrow$ answer is 2

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How many trivial relations can be formed on a set which has 64 elements?

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How many of the following statements are wrong

1. A relation is said to be reflexive on set A if each element in A is related to itself.

2. Empty relation defined on a non- empty set is reflexive

3. We can define a reflexive relation on A x B, where A is not a subset of B.

4. In a reflexive relation, all the elements should be of the form (a,a) for all a from the set on which the relation is defined

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