Question

Consider the function F(x,y,z) = ((x'y)'x'(zx)'(xy'+xz'))'

(a) Apply DeMorgan's theorem to the function F(x,y,z) that removes the complement outside the braces.
(b) Write the truth table of F(x,y,z).
(c) Draw the logic diagram of F(x,y,z).

Answer 1

DeMorgan's theorem can be applied to the given function F(x,y,z) to simplify it. The truth table of F(x,y,z) can be constructed to determine its outputs for different combinations of inputs. The logic diagram of F(x,y,z) can be drawn using logic gates.

Step-by-step explanation:

To apply DeMorgan's theorem to the function F(x,y,z) = ((x'y)'x'(zx)'(xy'+xz'))', we will remove the complement outside the braces:

F(x,y,z) = ((x'y)'x'(zx)'(xy'+xz'))' = (x+y)(x'+(z'+x))(x'+(y'+z))

Next, we can write the truth table of F(x,y,z) to determine its outputs for all combinations of inputs:

x y z F(x,y,z) 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1

Lastly, we can draw the logic diagram of F(x,y,z) using logic gates such as AND, OR, and NOT gates to represent the boolean operations: