For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct ? [take $$\triangle S$$ as change in entropy and w as work done]

A

$$\triangle S_{x \rightarrow z} = \triangle S_{x \rightarrow y} + \triangle S_{y \rightarrow z}$$

B

$$\triangle w_{x \rightarrow z} = \triangle w_{x \rightarrow y} + \triangle w_{y \rightarrow z}$$

C

$$\triangle w_{x \rightarrow y \rightarrow z} = \triangle w_{x \rightarrow y}$$

D

$$\triangle S_{x \rightarrow y \rightarrow z} = \triangle S_{x \rightarrow y}$$