Let there be a set A such that [imath] A = {1,2,3,...,2026} [/imath]
Then find the number of relations on set A such that it's reflexive, symmetric and has exactly (1013)² + (1013) - 2 elements.
The answer is [imath] \binom{2(1013)²-1013}{\frac{(1013)²-1013-2}{2}} [/imath].
Maybe we have to first include all the 2026 elements of the form [imath] (a,a) [/imath] and also the other ones which are reflexive so we will have [imath] \frac{\binom{2026}{2} - 2026}{2} [/imath] to choose from but then how should I proceed, if this is the right approach?
Thank you.
Then find the number of relations on set A such that it's reflexive, symmetric and has exactly (1013)² + (1013) - 2 elements.
The answer is [imath] \binom{2(1013)²-1013}{\frac{(1013)²-1013-2}{2}} [/imath].
Maybe we have to first include all the 2026 elements of the form [imath] (a,a) [/imath] and also the other ones which are reflexive so we will have [imath] \frac{\binom{2026}{2} - 2026}{2} [/imath] to choose from but then how should I proceed, if this is the right approach?
Thank you.