**Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.11**

Let $G$ be a group and $K \leq H \leq G$. Prove that $[G : K] = [G : H] \cdot [H : K]$.

Solution: See Lemma 3 of Exercise 3.2.10.

**Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.11**

Let $G$ be a group and $K \leq H \leq G$. Prove that $[G : K] = [G : H] \cdot [H : K]$.

Solution: See Lemma 3 of Exercise 3.2.10.