Computer Science
State whether the following expression is a Tautology, Contradiction or the Contingency with help of the truth table.
(X→Z) v ~[(X→Y) ^ (Y→Z)]
Boolean Algebra
ICSE 2016
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Answer
X→Z is equivalent to X'+ Z
| X | X' | Z | X'+Z |
|---|---|---|---|
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
X→Y is equivalent to X' + Y
| X | X' | Y | X'+Y |
|---|---|---|---|
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
Y→Z is equivalent to Y' + Z
| Y | Y' | Z | Y'+Z |
|---|---|---|---|
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| X→Y | Y→Z | (X→Y)^(Y→Z) | ~ |
|---|---|---|---|
| 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
| X→Z | ~[(X→Y) ^(Y→Z)] | (X→Z)v ~[(X→Y)^(Y→Z)] |
|---|---|---|
| 1 | 0 | 1 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
As all entries of column (X→Z) v ~[(X→Y) ^ (Y→Z)] is one hence, it is a Tautology.
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