Question

How many binary relations are there on a set of 3 elements?

Answer 1

Total number of  binary relation from n element set to itself is ${2n^2}$ i.e.n^2 entries with two choice take it or not.

${}$ ❤️

Answer 2

If a set A has n elements, A × A has $n^{2}$ elements, so there are $n^{2n}$ relations from A to A.

• The relation that exists between the elements in one set with the elements in another set is defined as the binary relation.
• The result of this binary relation will be another set that contains elements from both the input sets.
• When a set has n number of elements, then usually it has $n^{n}$ a relationship.
• Here, a set is of 3 elements, so to find the relations count first need to find out the total elements.
• $3^{2}$ = 9 is the total elements.
• Therefore, the number of relations will be $n^{2n}$.
• $3^{3*2}$ = $3^{6}$
• 729relation are there on 3element set.

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