Homework I

Tom Kelliher, CS 240

50 points, due Feb. 8

1. Use truth tables to verify each of the following:
   1. De Morgan's theorem for three variables: $\overline{XYZ} = \overline{X} + \overline{Y} + \overline{Z}$.

   2. $X + YZ = (X + Y)(X + Z)$ (Identity 15 from Feb. 1's notes).

   3. $\overline{X}Y +\overline{Y}Z +X\overline{Z} = X\overline{Y} + Y\overline{Z} + \overline{X}Z$

2. Use Boolean manipulation to verify each of the following:
   1. $\overline{X} \cdot \overline{Y} + \overline{X}Y + XY = \overline{X} + Y$

   2. $\overline{A}B + \overline{B} \cdot \overline{C} + AB + \overline{B}C = 1$

   3. $(X + Y)(X + \overline{Y}) = X$

   4. $X (X + Y) = X$

Tom Kelliher