Simplify the following using $\text{K}$ – map :
$F(A, B, C, D) = \Sigma (0, 1, 2, 8, 9, 12, 13)$
$d(A, B, C, D) = \Sigma (10, 11, 14, 15)$
$\text{d}$ stands for don't care condition.
- $A+\bar{B} \bar{D} +BC$
- $A+\bar{B} \bar{D} + \bar{B} \bar{C}$
- $\bar{A} + \bar{B} \bar{C}$
- $\bar{A} + \bar{B} \bar{C} + \bar{B} \bar{D}$