This was the first generation 3 inputs AND gate made of diode logic circuit. Silicon diode has a voltage drop = 0.6V
and regardless current I value .......
As one input = 3V , other 2 inputs are open, V = 1.4V = LOGIC LO
As one input = 2V, other 2 inputs are open, V = 2.4V = LOGIC LO
As one input = 1V, other 2 inputs are open, V = 3.4V = LOGIC HI
AS 3 inputs voltage as shown in drawing, V = LO , a AND gate function.
IF I = 4mA is given, THEN VOLTAGE DROP ON 1K ohm RESISTOR = 4V
THEREFORE. V = 5V - 4V = 1V
A SIMPLE MATH !