1. **State the problem:** We have a class of 30 music students. Among them, 13 play the piano, 16 play the guitar, and 6 play both instruments. We need to find how many students play neither the piano nor the guitar. 2. **Formula and rules:** To find the number of students who play neither instrument, we use the principle of inclusion-exclusion: $$\text{Number who play neither} = \text{Total students} - \text{Number who play piano or guitar}$$ where $$\text{Number who play piano or guitar} = \text{Number who play piano} + \text{Number who play guitar} - \text{Number who play both}$$ 3. **Calculate the number who play piano or guitar:** $$13 + 16 - 6 = 23$$ 4. **Calculate the number who play neither:** $$30 - 23 = 7$$ 5. **Answer:** **7 students** play neither the piano nor the guitar.