I just can't wrap my head around why this statement does not hold:
∃x∃yRxy ⊨ ∃x∃yRyx
Let D = {1, 2} and Let I(R) = {(1,2)}
M ⊨ ∃x∃yRxy = 1, since some x(1) has some y(2) such that (x,y) ∈ I(R)
But in my eyes:
M ⊨ ∃x∃yRyx = 1, since some x(2) has some y(1) such that (y,x) ∈ I(R)
Or does this not hold because I(R) = x,y so:
M ⊨ ∃x∃yRyx = 0, since some x(1) has some y(2) such that (y,x) ∈ I(R)