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I want to find the DNF of the following expression but it got all messy.

I also tried it in wolfram alpha, and of course it showed i really need the steps you need to make to get there $\dots$

This is the table I got: disjunctive normal form

$$\boxed{\begin{array}{cccc}x&y&z&f(x,y,z)\\\text{T}&\text{T}&\text{T}&\text{T}\\\text{T}&\text{T}&\text{F}&\text{T}\\\text{T}&\text{F}&\text{T}&\text{T}\\\text{T}&\text{F}&\text{F}&\text{T}\\\text{F}&\text{T}&\text{T}&\text{F}\\\text{F}&\text{T}&\text{F}&\text{T}\\\text{F}&\text{F}&\text{T}&\text{F}\\\text{F}&\text{F}&\text{F}&\text{F}\end{array}}$$

any ideas to how this could be done ?

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  • $\begingroup$ Can you please edit your post and explain what is DNF? $\endgroup$
    – Ertxiem - reinstate Monica
    Commented Dec 4, 2019 at 10:17
  • $\begingroup$ cant really explain, English is not my native, but $\endgroup$
    – hotdogmeal
    Commented Dec 4, 2019 at 10:23
  • $\begingroup$ Disjunctive normal form (dnf) is the normalization of a logical formula in Boolean mathematics. In other words, a logical formula is said to be in disjunctive normal form if it is a disjunction of conjunctions with every variable and its negation is present once in each conjunction $\endgroup$
    – hotdogmeal
    Commented Dec 4, 2019 at 10:23
  • $\begingroup$ You can try to use a Karnaugh map $\endgroup$
    – Ethan
    Commented Dec 4, 2019 at 10:27
  • $\begingroup$ i dont know how to use kmap $\endgroup$
    – hotdogmeal
    Commented Dec 4, 2019 at 10:38

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