F (x,y,z) = ¬x¬y , and G(x,y,z) = ¬(x + y)
is F(x,y,z) = G(x,y,z) ?
Will we get the same truth table output?
This is the truth table outputs that I got and it’s not equal but others say it equal, I’m not sure how can it be equal?
F(x,y,z) = not x and not y Both x and y need to be 0 And z is ignored.
G(x,y,z) = not (x or y) At least one of x or y need to be 0 And z is also ignored.
Am I doing something wrong here?
"not x" is true if x is false. "not y" is true if y is false. So, "not x and not y" is true only if both x and y are false.
On the other hand, "not (x or y)" is true if the entire expression inside the parentheses (x or y) is false. This happens only when both x and y are false.
Therefore, "not x and not y" is logically equivalent to "not (x or y)." or, ¬x∧¬y is equivalent to ¬(x∨y) in terms of boolean logic.