Creation of a logic circuit with stipulations

Question

I can only use the four sources A, B, C and D. I'm allowed to use negations, if needed.

The stipulations are:

1. If "A" is not on, then no combination of BCD are allowed to produce an output
2. "A" plus two other sources have to produce an output
3. "A" plus three other sources have to produce an output
4. "A" plus one source, is not allowed to produce an output

In short, if "A" is off, then there can never be an output. If "A" is with only one other source, then there can never be an output. All other combinations MUST produce an output.

I've been at this for almost 3 hours now and I cannot figure it out. Every time I get almost every stipulation satisfied, I hit a roadblock that messes something up.

Answer 1

So you want an output if $A$ and at least two of $B,C,D$. Written like this we can transcribe it as $$A \wedge ((B \wedge C)\vee (B \wedge D) \vee (C \wedge D))$$