Hi, We have this logic gate question that I cannot figure out howto solve: Four

Question

Hi,
We have this logic gate question that I cannot figure out howto solve:
Four water lines cool a reactor. If fewer than two linesare open, there is a risk of overheating the reactor. Using AND,OR, and NOT gates, design a circuit that shuts down the reactor(output=0) if fewer than two water lines are turned on.
At this point, even a clue as to how to start the problemwould be so helpful. I've tried working on this for multiple hours,and I cannot get a solution (I can get to a point where only 1 or 2truth table answers are incorrect). I've tried grouping the inputs(A, B) together and (C,D) together and joining them, as well asstarting with two inputs and cascading the rest into thecircuit.
Thanks so much for your help!!
We have this logic gate question that I cannot figure out howto solve:
Four water lines cool a reactor. If fewer than two linesare open, there is a risk of overheating the reactor. Using AND,OR, and NOT gates, design a circuit that shuts down the reactor(output=0) if fewer than two water lines are turned on.
At this point, even a clue as to how to start the problemwould be so helpful. I've tried working on this for multiple hours,and I cannot get a solution (I can get to a point where only 1 or 2truth table answers are incorrect). I've tried grouping the inputs(A, B) together and (C,D) together and joining them, as well asstarting with two inputs and cascading the rest into thecircuit.
Thanks so much for your help!!

Explanation / Answer

Given function gives zero when fewer than two water lines areon. F(A, B, C, D) = ABC'D' + AB'CD' + AB'C'D + A'BCD' + A'B'CD + A'BC'D+ ABCD' + ABC'D + AB'CD +A'BCD                           + ABCD                      = ABD'(C+C') + AC'D (B + B')+ AB'C (D+D') + A'BC(D+D') + A'D(BC'+B'C) + ABCD                   = ABD' + AC'D + AB'C+ A'BC + A'D (B.C)' + ABCD                 This function gives zero when less than 2 water lines areon.....

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