We have to prove that a combination of 3 NAND gates is logically equivalent to an OR gate by using a truth table. I thought this one was going to be easy but maybe I'm overthinking it a bit. I feel like I may have proved it's equal to a NOR instead of an OR. Can somebody check over this for me? From reading up on NAND gates I can see that it's just the reverse order of an OR gate (i.e if OR = 0,1,1,1 then NAND = 1,1,1,0).Assume there are 2 inputs, and we run them through 2 seperate NAND gates and then run those two outputs to a final NAND gate(3 total NAND gates).

x y x OR y ~x ~y (x AND y) ~(x AND y) (~x OR ~y) 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0

Is this correct? The thing that was jumbling me up is that I was unsure of things like "is NAND written as ~(A ^ B) or (~A ^ ~ B)". Did I just prove it was equal to a NOR gate instead of an OR?