A NOR gate is an inverted OR gate. This is the same as using the output of the OR gate as the input to the NOT gate. This means that the NOR gate returns TRUE only when both inputs are FALSE.

Input 1	Input 2	Output
Input 1 0	Input 2 0	Output 1
Input 1 0	Input 2 1	Output 0
Input 1 1	Input 2 0	Output 0
Input 1 1	Input 2 1	Output 0

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Empty Example:
nor|[]~[]

Filled-In Example:
nor|[reskillable:mining|5]~[reskillable:gathering|5]

Only allow using a wooden shovel until the player gets mining or gathering level 5:

ZenScript
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addRequirement(<minecraft:wooden_shovel:*>, "nor|[reskillable:mining|5]~[reskillable:gathering|5]");