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Question
State and prove De Morgan’s first and second theorem.
Answer in Brief
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Solution
First Theorem: The complement of the sum is equal to the product of its complements.
`overline("A" + "B") = overline"A".overline"B"`
| A | B | A + B | `overline("A" + "B")` | `overline"A"` | `overline"B"` | `overline"A".overline"B"` |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
Second Theorem: The complement of the product of two inputs is equal to the sum of its complements.
`overline("A"."B") = overline"A" + overline"B"`
| A | B | A.B | `overline("A"."B")` | `overline"A"` | `overline"B"` | `overline"A" + overline"B"` |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
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De Morgan’s Theorem
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Chapter 10: Electronics and Communication - Evaluation [Page 248]
