On Birkhoff's quasigroup axioms

Birkhoff defined a quasigroup   as an algebra (Q,⋅,\,/)(Q,⋅,\,/) that satisfies the following six identities: x⋅(x\y)=yx⋅(x\y)=y, (y/x)⋅x=y(y/x)⋅x=y, x\(x⋅y)=yx\(x⋅y)=y, (y⋅x)/x=y(y⋅x)/x=y, x/(y\x)=yx/(y\x)=y, and (x/y)\x=y(x/y)\x=y. We investigate triples and tetrads of identities composed of these six, emphasizing those that axiomatize the variety of quasigroups.