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प्रश्न
Verify using truth table, DeMorgan's theorem for three variables.
सविस्तर उत्तर
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उत्तर
For the sum form, [(A+B+C)'=A'B'C']. The two sides have identical values in every row. The dual product form is [(ABC)'=A'+B'+C'].
| A | B | C | A+B+C | (A+B+C)' | A' | B' | C' | A'B'C' |
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
Since the columns [(A+B+C)'] and [A'B'C'] are identical, the theorem is verified.
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