Question about AND gate using diodes
If the voltage across the diode is equal to its \$V_f\$ (what you call \$V_{ON}\$) and no current is flowing through it then the diode is on the knife edge between forward and reverse bias. For forward bias we usually assume a positive current flowing through the diode and for reverse bias we assume that \$V_D &lt; V_f\$.

Since the initial conditions (\$V_A = V_{SOURCE}\$ and \$V_{OUT} = 0V\$) have the diode reverse biased I would probably call it reverse biased even when the output voltage rises to the source voltage.