How will you conclude that the same potential difference (voltage) exists across three resistors connected in a parallel arrangement to a battery?
Potential difference in any part of a circuit is equal to the difference in the potentials of the start and end point of the part of circuit being considered. Parallel circuits are defined as the circuits that have common start and end points. The starting point of all the parallel circuits being the same, the potential at their start point is also same. Similarly, the potential of the end point of all the parallel circuit is also same. The potential of start and end point of all parallel circuits being same, their potential difference is also same.