In the shown below circuits, I understand the operation of the circuit but I cannot figure out why are we using diodes? I mean if the diodes are missing the circuit will still be valid and the truth table will still be true?? or am I missing something?

 

The inputs of the gate are at A and B (the RHS of the switch and not before the switch). If there were no diodes after A and B, when A becomes high, the high would be shorted to B making both A and B high.

Allen

 

The illustrations are not really good at explaining the concept.
Imagine figure a-b where the input is from two logic gates, if you just tie the gate outputs together and assert one high and the other low, they will fight, get hot, and produce an undefined output state.

In scenario D, suppose that the battery was dry cell stack that was not of the rechargeable variety, without the diodes it would be subject to the power supply voltage and potentially be damaged by charging currents. Without the diodes how could you control which part powered the circuit? With the diodes, the higher voltage wins out automatically.