Explain the statement: "$V \to I$ relation is not always a one-one function."

(A) function is one-one if every input value maps to a unique output value. In the context of electrical circuits, the $V \to I$ relation represents the current $I$ as a function of voltage $V$.
For an Ohmic conductor, the relationship is linear $(V = IR)$, meaning for every $V$, there is a unique $I$, making it a one-one function.
However, for non-Ohmic devices (like $p-n$ junction diodes or thermistors), the $V-I$ characteristic curve is non-linear.
Specifically, in devices exhibiting negative differential resistance (like a tunnel diode), the current $I$ may decrease as voltage $V$ increases over a certain range.
Furthermore, in devices with hysteresis or complex $V-I$ characteristics, multiple values of $V$ might correspond to the same value of $I$, or the relationship may not be strictly monotonic.
Therefore, because the current does not always increase uniquely and monotonically with voltage across all types of materials, the $V \to I$ relation is not universally a one-one function.