I am working with boolean algebra for my Navy coursework and I was wondering if anyone knew what the formula for $A^c \cap B^c \cap C^c$ is? Also does $A^c \cap B^c \cap C^c = (A \cap B \cap C)^c$?
The reason why I ask this is because there was a problem on an assessment that asked what three following inputs in a NAND gate would produce the desired output and it listed 4 options. The only right answer was three HIGHS (1) produced a LOW (0) in a NAND gate, but I selected three LOWS (0) produced a HIGH (1).
Draw a Venn Diagram and we can readily see that $$ A^c \cap B^c \cap C^c = (A\cup B\cup C)^c $$