voltage - Why is base resistor of a transistor important?

I know that this is a very basic question but I really do not know the answer.

I was making simple logic gates using transistors and I used PNP transistor as NOT gate.

I made the following circuit: (A) AND (B) AND (NOT C)

This circuit does not work without the resistors R1,R2 and R3. Why are these resistors important ?

^{simulate this circuit – Schematic created using CircuitLab}

The Following NOT gate does not need a base resistor. I connect Vcc or ground directly to base and it works.

How can it work without resistors although it is very similar to the previous circuit ?

^{simulate this circuit}

Answer

Without resistors, your circuit looks like

^{simulate this circuit – Schematic created using CircuitLab}

The problem is that there is no voltage across the emitter-base of Q1, so it cannot turn on.