ΔSX→Z=ΔSX→Y+ΔSY→Z
ΔWX→Y→Z=ΔWX→Y
ΔSX→Y→Z=ΔSX→Y
ΔWX→Z=ΔWX→Y+ΔWY→Z
Entropy is a state function. Its value is independent of the path followed. Therefore, the change in entropy from state X to state Z is the same regardless of the path taken. This means ΔSX→Z = ΔSX→Y + ΔSY→Z is correct. Work, however, is a path function. The work done depends on the path taken. Therefore, ΔWX→Y→Z ≠ ΔWX→Z.