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The pull-down resistors are to keep the logic level going into the gate at ground until the button is pushed.
IC's are VERYY sensitive to ESD (Electrostatic) and if you leave the inputs 'floating' (not conected) they will pick up signals from a range of things...
and you dont tie the input straight to ground to keep it at logic 0 because when when you press the button you will make a short circuit.
The resistor acts as a load.
It is a high value resistor to heavily limit current, but the IC will still pick up the logic levels.
You can change the resistor value to 10K if you want.
You are "giving" 9V to the CMOS input pin when the switch is closed. If it were not for the 10k pull-down resistor, then when the switch is open, the CMOS input pin would be floating, i.e. "undefined", some times low, some times high, and sometimes ???.
With the resistor there, the 10K discharges the input capacitance of the CMOS input pin to ground, putting a defined low logic state there. Even 10K is a very low impedance compared to the input inpedance of a floating CMOS pin.
The rule is: NEVER, EVER leave a CMOS input pin floating!!!
CMOS is nice in that you can use pull-down resistors as well as pull-up resistors. Pull-down resistors never worked well in TTL logic because they had to be of such low value to pull the input down to a valid logical LOW. It's a lot harder to pull a TTL input down than it is to pull up because the voltage range of a logical LOW is a lot narrower than is the voltage range for a logical HIGH. If you HAD to pull down with TTL, it was best accomplished by pulling UP on the input of an inverter and feeding the inverter output to the intended input to be pulled down.
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