Question

The number of binary relations on a set with $n$ elements is

• A. $n^2$
• B. $2n$
• C. $2^{n^2}$
• D. None of these

Answer 1

The correct option is C $2^{n^2}$

The maximum number of elements in a binary relation on a set $A$ with $n$ elements = Number of elements in $A\times A=n^2$
Each element has two choices, either to appear on a binary relation or doesn't appear on a binary relation.
$\therefore$ Number of binary relations $=2^{n^2}$.