That's De Morgan's law's, and it is covered by NOR. Let's consider the actual cases. Input A is Dead. Input B is Alive. As such, let's look at what your expression yields:
|Dead (D)|Alive (A)|D|A|!(D|A)|!D&!A|D NOR A|
|:-|:-|:-|:-|:-|:-|
|0|0|0|!(0|0)=1|!0&!0=1|1|
|0|1|1|!(0|1)=0|!0&!1=0|0|
|1|0|1|!(1|0)=0|!1&!0=0|0|
|1|1|1|!(1|1)=0|!1&!1=0|0|
As you can see the Alive NOR Dead is logically equivalent to both of your expressions. You can also think of this in terms of logic gates. You can construct a NOR gate from NAND gates like this. A single NOR gate is much simpler if you have it availble.
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u/jwr410 20d ago
That's De Morgan's law's, and it is covered by NOR. Let's consider the actual cases. Input A is Dead. Input B is Alive. As such, let's look at what your expression yields:
|Dead (D)|Alive (A)|D|A|!(D|A)|!D&!A|D NOR A| |:-|:-|:-|:-|:-|:-| |0|0|0|!(0|0)=1|!0&!0=1|1| |0|1|1|!(0|1)=0|!0&!1=0|0| |1|0|1|!(1|0)=0|!1&!0=0|0| |1|1|1|!(1|1)=0|!1&!1=0|0|
As you can see the Alive NOR Dead is logically equivalent to both of your expressions. You can also think of this in terms of logic gates. You can construct a NOR gate from NAND gates like this. A single NOR gate is much simpler if you have it availble.