I have the following problem:
Simplify the following Boolean functions by algebraic transformation. Express the result in disjunctive normal form (DNF).
i) $j(a, b, c, d)=a \bar{b}+c+\bar{a} \bar{c} d+b \bar{c} d$
ii) $k(a, b, c, d)=\overline{\bar{a} b \bar{c}} \cdot \overline{a \bar{b} \bar{c}}$
iii) $l(a, b, c, d)=a b c+a b \bar{d}+a \bar{c}+\bar{a} \bar{b} \bar{c} d+\bar{a} c$
iv) $m(a, b, c, d)=(a+\bar{b}+c) \cdot \overline{a b+\bar{a} \bar{c}}$
For this I have the rules shown below at hand:
Note: $+$ means or and $*/\text{no dot}$ means and.
I would now be interested, since I have been trying my hand at these tasks for some time now, if there is a structured approach to this. Or is it here like with the application of binomial formulas that one must recognize the laws?