Give the products formed from the reactions of each of the following compounds with: i. `KMnO_4` in warm acid
ii. `O_3//H_2O`
a. Pent-1-yne
b. Nona-2, 6-diyne
c. Hex-3-yne
d. 2-Methylhept-3-yne

Explanation

To solve the problem, we will analyze the reactions of the given alkynes with `KMnO4` in warm acid and `O_3` in the presence of water. Both reactions involve oxidation of the triple bond in alkynes, leading to the formation of carboxylic acids.

### Step-by-Step Solution:

**a. Pent-1-yne (C5H8)**

1. **Structure of Pent-1-yne**:
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