Question

Show that  \[AB + \overline {AB }\]  is always 1.

Answer 1

Given:

\[X = AB + \overline {AB}\]

Let:
AB = y
∴ \[X = y + \overline{y}\]

 

For y = 0,
X = 0 + 1
   = 1

For y = 1,
X = 1 + 0
   = 1

Thus, X = 1 for all values of y = AB.