Static circuit analysis

[username]

I need help with the following question:

For the circuit in attach 1, determine the logic function and minimum resistance value of the resistor Rcmin such that the output transistor is in saturation state when it is on.
If the output transistor is charged with capacitor Cp=220nF, determine the fall and rise time of the output voltage.
Given data: ?min=50, ?=100, Vcc=5V, Ubet=0.5V, Ubes=0.7V, Ube=Ud=0.6V, Uces=0.2V.

Note: This is not homework, I am practicing for exam.

Attempt:
We consider the static analysis of a circuit (low and high logic level).

Note: I assumed that diodes are idealized (when it is forward biased the voltage is 0.6V, and when it is reverse biased, it is an open branch).

1. Low logic level (Vin=0V)
We don't consider this case because we can never have Vin=0V.
Is this correct?

2. High logic level (Vin=Vcc=5V)
We conclude that at least one input diode is forward biased.
Fourth diode (that is connected to emitter of input voltage) is reverse biased.
Output transistor is on. We need to check if it is in saturation state.
The condition is Ics>Ib/?min. We can find Ib as Ib=Ubes/5k=0.14mA and Ics as Ics=Uces/Rcmin. This gives that Rcmin>200/7 ?.
Is this correct?

Where to connect capacitor Cp and how to find fall and rise time of Vout?
What is the value of Vout in this case?
How to determine the logic function of this circuit?

[sentry7]

Well to determine the logic function, try constructing a truth table. Toggle va, vb, and vc HI and LO and for each case, look at the equivalent circuit and find the voltage (HI or LO) at the output.