Four couples go ballroom dancing one evening. Their first names are Henry, Peter, Louis, Roger, Elizabeth, Jeanne,  Mary,  and  Anne.  If  Henry's wife is not dancing with her husband (but with Elizabeth's husband), Roger and Anne are not dancing,  Peter is playing the trumpet,  and  Mary is playing the piano,  and  Anne's husband is not  Peter, who is  Roger's wife?

$\textbf{(A) } \text{Elizabeth} \quad\textbf{(B) }\text{Jeanne}\quad\textbf{(C) }\text{Mary}\quad\textbf{(D) }\text{Anne}$
1. **Identify the dancers and non-dancers:**
   - Henry's wife is dancing with Elizabeth's husband.
   - Roger and Anne are not dancing.
   - Peter is playing the trumpet.
   - Mary is playing the piano.
   - Anne's husband is not Peter.

2. **Determine Elizabeth's husband:**
   - Since Elizabeth's husband is dancing, he cannot be Roger (not dancing), Peter (playing the trumpet), or Henry (his wife is dancing with Elizabeth's husband).
   - Therefore, Elizabeth's husband must be Louis.

3. **Determine Henry's wife:**
   - Henry's wife is dancing with Elizabeth's husband (Louis).
   - Henry's wife cannot be Anne (not dancing), Mary (playing the piano), or Elizabeth (married to Louis).
   - Therefore, Henry's wife must be Jeanne.

4. **Determine Anne's husband:**
   - Anne's husband is not Peter.
   - Since Louis and Henry already have their partners (Elizabeth and Jeanne, respectively), the only remaining option is Roger.

5. **Determine Roger's wife:**
   - Since Roger is Anne's husband, Roger's wife is Anne.

Thus, the answer is $\boxed{\text{Anne}}$.