`(KOOC-CH=CH-COOK)` undergoes Kolbe's reaction to form a product which reacts with ammoniacal `AgNO_3` solution to form a precipitate.
The product is a saturated hydrocarbon that forms salt with `AgNO_3`.

Options

A. If both `(A)` are `( R)` are true and `( R)` is the correct explanation of `(A)`.
B. If both `(A)` and `( R)` are true but `( R)` is not the correct explanation of `(A)`.
C. If `(A)` is true but `( R)` is false.
D. If `(A)` is false but `( R)` is true.

Explanation

To solve the given question step by step, we will analyze the reaction of the compound `(KOOC-CH=CH-COOK)` (potassium salt of a carboxylic acid) undergoing Kolbe's electrolysis reaction and its subsequent reaction with ammoniacal `AgNO3`.

### Step 1: Identify the Compound
The compound given is `(KOOC-CH=CH-COOK)`, which is the potassium salt of 2-butenoic acid. This compound has two carboxylate groups (–COOK).

### Step 2: Kolbe's Electrolysis Reaction
In Kolbe's electrolysis, the carboxylate ions (from the two carboxylic acid groups) are oxidized at the anode. The reaction can be summarized as follows:
- Each carboxylate ion will lose a carbon dioxide molecule (CO2) and will couple to form a new carbon-carbon bond.

For the given compound, the reaction will produce:
- 2 moles of CO2 (one from each carboxylate group).
- A product that is an alkyne (since the original compound has a double bond).

### Step 3: Determine the Product
The product formed from the Kolbe's electrolysis of `(KOOC-CH=CH-COOK)` will be an alkyne. Specifically, it will be 1-butyne (CH≡C-CH2-COOH) after the loss of CO2.

### Step 4: Reaction with Ammoniacal AgNO3
The product formed (1-butyne) can react with ammoniacal `AgNO3`, which is known as Tollens' reagent. This reagent is used to test for terminal alkynes. The reaction will lead to the formation of a silver acetylide precipitate.

### Step 5: Conclusion
The assertion states that the product is a saturated hydrocarbon that forms a salt with `AgNO3`. However, since the product is an alkyne (which is an unsaturated hydrocarbon), the assertion is correct, but the reason is incorrect. Therefore, the correct answer is option C: Assertion is correct, reason is wrong.