Computer Science
Obtain the truth table to verify the following expression:
X.(Y + Z)= X.Y + X.Z
Also state this law.
Boolean Algebra
53 Likes
Answer
This is Distributive Law.
Truth Table
| X | Y | Z | Y+Z | X.(Y+Z) | X.Y | X.Z | X.Y+X.Z |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
As columns X.(Y+Z) and X.Y+X.Z have same values, hence the expression is proved.
Answered By
28 Likes
Related Questions
Show that dual of P'QR' + PQ'R + P'Q'R is equal to the complement of PQ'R + Q.(P'R' + PR')
What are maxterms? Convert the following function as a product of maxterms:
F(P, Q, R)= (P + Q).(P' + R')Given F = A + (B + C).(D' + E)
Find F' and show the relevant working in steps.For the given truth table A, B and C are the inputs and X is the output.
A B C X 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 Write:
(i) Canonical Sum of Product expression (SOP).
(ii) Canonical Product of Sum expression (POS).