Consider the following in Boolean Algebra
X: a ∨ (b ∧ (a ∨ c)) = (a ∨ b) ∧ (a ∨ c)
Y: a ∧ (b ∨ (a ∧ c)) = (a ∧ b) ∨ (a ∧ c)
a ∨ (b ∧ c) = (a ∨ b) ∧ c is satisfied if
Solution
It does depend on any of the cases i.e., X or Y as it is not satisfied any of the property of Boolean algebra.
We can solve the equation as shown below:
| a |
b |
c |
b ∧ c |
a ∨ (b ∧ c) |
a ∨ b |
(a ∨ b) ∧ c |
| 0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 0 |
0 |
1 |
0 |
0 |
0 |
0 |
| 0 |
1 |
0 |
0 |
0 |
1 |
0 |
| 0 |
1 |
1 |
1 |
1 |
1 |
1 |
| 1 |
0 |
0 |
0 |
1 |
1 |
0 |
| 1 |
0 |
1 |
0 |
1 |
1 |
1 |
| 1 |
1 |
0 |
0 |
1 |
1 |
0 |
| 1 |
1 |
1 |
1 |
1 |
1 |
1 |
Hence, the correct answer is option 4.