CBSE Class 11 Computer Science
Question 42 of 68
Data Representation and Boolean Logic — Question 13
Back to all questionsThe first law states that when two (or more) input variables are OR'ed and negated, they are equivalent to the AND of the complements of the individual variables.
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Proof using truth table:
| A | B | A' | B' | A + B | (A+B)' | A'.B' |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 |
The second law states that when two (or more) input variables are AND'ed and negated, they are equivalent to the OR of the complements of the individual variables.
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Proof using truth table:
| A | B | A' | B' | A.B | (A.B)' | A' + B' |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 |