Question

how will you conclude that the same potential difference exists across three resistors connected in a parallel arrangement to a battery

Answer 1

we can conclude that the same potential difference exists across three resistors connected in a parallel arrangement to a battery by following steps

1. First connect a voltmeter across the one of the resistance let R1 and note down the voltage V1
2. Then remove the voltmeter from the resistance R1 and now connect to the R2 and note down the voltage V2
3. Now again remove the voltmeter from the resistance R2 and now connect to the R3 and note down the voltage V3
4. In the end you will found that all the voltages are same V1=V2=V3=V

Answer 2

see in the attachment below