Answer by k_v for How may I define e.g. Tilde[x,y] to have certain properties?

Note that "~" is used in Mathematica for infix form of operators and it isn't the same as Tilde which could be inputted as [Esc]~[Esc]

ClearAll@TildeTilde /: Tilde[x_, x_] := TrueSetAttributes[Tilde, Orderless]Tilde /: Tilde[x_, y_ ] && Tilde[y_, z_ ] := Tilde[x, z]

I added one more defenition to Tilde for the case when x, y are not the same