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I have seen two observations from the paper by Har-Peled but I do not know how to prove them (i) If $C1$ and $C2$ are the $(k, ε)$-coresets for disjoint sets P1 and P2 respectively, then $C1 ∪ C2$ is a $(k, ε)$-coreset for $P1 ∪ P2$. (ii) If $C1$ is $(k, ε)$-coreset for $C2$, and $C2$ is a$(k, δ)$-coreset for $C3$, then $C1$ is a $(k, ε+δ)$- coreset for $C3$

Can anyone please figure it out?

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