Discrete mathematics - Reflexive, Symmetric, Anti Reflexive

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Question, I know there are formulas for Reflexive relations, which is the $2^{n^2-n}$.
And for Symmetric: $2^\frac{n^2+n}{n}$
I saw a video of Anti Reflexive, and there was the same calculation when A was: $A={(1,2,3,4)}$
They calculated the Anti reflexive, and it was the same as the reflexive relation.
I mean, the number of relations of Anti-Reflexive was $2^{12}$ Which is the same as Reflexive relations $2^{12}$.

Could I say the number of Anti-Reflexive relations and number of Reflexive relations are the same? ( Basically the question for summarize )