In this question, we are given two statements: an Assertion (A) and a Reason (R). Our goal is to determine the relationship between them and select the most appropriate answer.

Assertion (A): The gate of a MOSFET is insulated from the body of FET by deposition of a very thin fragile layer of \(\text{SiO}_2\) over the substrate.

Reason (R): The device is therefore called an insulated gate field-effect transistor (IGFET).

Explanation:

1. The term "MOSFET" stands for Metal-Oxide-Semiconductor Field-Effect Transistor. The gate of a MOSFET is insulated from the rest of the device by a thin oxide layer, typically silicon dioxide (\(\text{SiO}_2\)), which serves as an insulator. This is exactly what the Assertion (A) states—indicating the insulating nature of the oxide layer.
2. Due to this insulating property of the gate achieved through the deposition of \(\text{SiO}_2\), the MOSFET is also known as an Insulated Gate FET (IGFET). This is because the gate does not make direct contact with the conductive channel; instead, it is separated by an insulating oxide layer, which Reason (R) describes.
3. Both Assertion (A) and Reason (R) are correct. Furthermore, Reason (R) correctly explains the Assertion (A) because the terminology of "insulated gate" directly arises from the structural characteristic described in the Assertion.

Conclusion:

Thus, the correct answer is: Both (A) and (R) are correct and (R) is the correct explanation of (A).