An organic compound `(A)` on treatment with ethyl alcohol gives a carboxylic acid `(B)` and compound `( C)`. The hydrolysis of `( C)` under acidic conditions gives `(B)` and `(D)`. Oxidation of `(D)` with `KMnO_4` also gives `(B)`. `(B)` on heating with `Ca(OH)_2` gives `(E)` (molecular formula, `C_3 H_6 O`). `(E)` does not give Tollens test and does not reduce Fehling's solution but forms a `2,4-`dinitrophenyl hydrazone. Identify `(A),(B), ( C), (D)`, and `(E)`.

Explanation

To solve the problem step-by-step, we will analyze the information given in the question and deduce the identities of compounds A, B, C, D, and E.

### Step 1: Identify Compound E
The molecular formula of compound E is given as C₃H₆O. The information states that E does not give Tollens' test and does not reduce Fehling's solution, which indicates that E is likely a ketone. The only ketone with the formula C₃H₆O is propan-2-one (also known as acetone).

**Compound E = Propan-2-one (CH₃COCH₃)**

### Step 2: Determine the Reaction of B with Ca(OH)₂
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