I want to convert p ∧ (p→q) into conjunctive form.

I started like this:

P ∧ (¬p ∨ q)

But I'm not sure how to continue and how to change this formula to conjunctive normal form.


Then use distributivity and wolframalpha

$p ∧ (p→q) \leftrightarrow p ∧ (¬p ∨ q) \leftrightarrow (p ∧ ¬p) ∨ (p ∧ q) \leftrightarrow \text{false} ∨ (p ∧ q) \leftrightarrow p ∧ q$

  • $\begingroup$ I don't think this answer will help the OP to solve the next problem he will encounter. And why doyou add a link to Wolframalpha? $\endgroup$ – miracle173 Aug 4 '19 at 9:25
  • $\begingroup$ I think this is exactly the step, where our friend sciuni chalaka got stuck. The link to wolframalpha provides a quick method for verification $\endgroup$ – Ahmed Hossam Aug 4 '19 at 9:29

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