Homework SourseWhy does BAACD simplifie to BACD SolutionBAACD simplifies to
Why does B(A+A\'CD) simplifie to B(A+CD) ?
Solution
B(A+A\'CD) simplifies to B(A+CD)
We need to focus on (A+A\'CD) which is simplified to (A+CD)
It followed boolean theorem A + A\'B = A + B (by More two-variable theorems)
In our case B is CD.
Following is the truth table to know that A + A\'B = A + B
Since A + A\'B and A + B got the same values, A + A\'B can be simplified to A + B and
B(A+A\'CD) simplifies to B(A+CD)
| A | B | A\' | A\'B | A+A\'B | A+B |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 |
