**Ohm's Law:**

Ohm's law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points. Mathematically, it is represented as:

V = I * R

Where:
V = Voltage (in volts)
I = Current (in amperes)
R = Resistance (in ohms)

**Effect of Reducing Voltage on Resistance:**

When the voltage across a resistor is reduced, it affects the current flowing through the resistor according to Ohm's law. However, the resistance value remains unchanged.

**Explanation:**

To understand why the resistance remains constant, let's consider the relationship between voltage, current, and resistance in Ohm's law.

V = I * R

Now, if we reduce the voltage by half, the new voltage (V') can be expressed as:

V' = V/2

Substituting this into Ohm's law equation, we have:

V'/2 = I * R

Since the resistance (R) is a constant value for a given resistor, we can rewrite the equation as:

(V/2) = I * R

Comparing this equation with the original Ohm's law equation, we can see that the current (I) will be halved when the voltage is reduced by half.

So, reducing the voltage to half will result in only half the current flowing through the resistor, while the resistance value remains the same.

**Conclusion:**

Therefore, in accordance with Ohm's law, if the voltage across a resistor is reduced to half, the resistance (R) remains unchanged. Option (1) "Remain unchanged" is the correct answer.