Synthesis of cyclohexane -1,2 diol from cyclohexene may be accomplished in two ways :
I . `MnO_(4)` dilute `OH, O^(@)C` dihydroxylation
II . Peracid epoxidation followed by NaOH opening of the epoxide ring .
Which of the following statement about the products from these reactions is correct ?

Options

A. Methods I and II give same product
B. Method I gives resolvable racemic mixture while method II will give non- resolvable achiral product
C. Method I gives resolvable optically inactive compound while method II gives resolvable racemic mixture
D. Products obtained through method I and II will have diasteriomeric relationship

Explanation

To synthesize cyclohexane-1,2-diol from cyclohexene, we can use two different methods. Let's analyze each method step by step.

### Method I: Dihydroxylation using MnO4 in dilute OH
1. **Reagent and Conditions**: We use dilute potassium permanganate (KMnO4) in the presence of hydroxide ions (OH-) at 0 degrees Celsius.
2. **Mechanism**: This reaction involves syn-dihydroxylation, where both hydroxyl (OH) groups add to the same side of the double bond in cyclohexene.
3. **Product Formation**: The product formed is cyclohexane-1,2-diol, where both OH groups are on the same side (cis configuration).

### Method II: Epoxidation followed by Ring Opening
1. **Reagent and Conditions**: We use a peracid (like m-chloroperbenzoic acid) to epoxidize cyclohexene, forming an epoxide.
2. **Mechanism**: The epoxide ring is then opened using sodium hydroxide (NaOH), which leads to anti-dihydroxylation. This means that the two hydroxyl groups will add to opposite sides of the double bond.
3. **Product Formation**: The product formed is also cyclohexane-1,2-diol, but in this case, the OH groups are on opposite sides (trans configuration).

### Comparison of Products
- **Method I** results in a **cis-1,2-diol** (syn addition).
- **Method II** results in a **trans-1,2-diol** (anti addition).

### Conclusion
Now, let's evaluate the statements regarding the products from these reactions:
1. **Statement 1**: Method 1 and Method 2 give the same product. **(Incorrect)**
2. **Statement 2**: Method 1 gives a resolvable racemic mixture while Method 2 gives a non-resolvable chiral product. **(Incorrect)**
3. **Statement 3**: Method 1 gives a resolvable optically inactive compound while Method 2 gives a resolvable compound. **(Correct)**

Thus, the correct answer is **Option 3**.