Please give me feedback for my answer to this question.

Question: (1) Are the boolean functions $(p \land \neg q) \lor ( \neg r \land q)$ and $(p \lor \neg q) \land (r \lor \neg q)$ equal?. Explain your answer.

My Answer: -

No, they are not equal because they are different. By computing $p=1, q=1, r=1$ into the functions, then $(p \land \neg q) \lor ( \neg r \land q) = 0$ and $(p \lor \neg q) \land (r \lor \neg q) = 1$. Therefore, they are not equal because their outcome is different.

Same if I compute $p=0, q=0, r=0,$ they will not equal.

  • $\begingroup$ That's really difficult to read because you mix logical conjunctions with natural language particles. $\endgroup$ – mathse Apr 14 '14 at 22:54
  • 1
    $\begingroup$ Yeah, it was. I've added $\LaTeX$ to make things clearer. $\endgroup$ – Graham Kemp Apr 14 '14 at 22:57

Your reasoning is completely correct. You have demonstrated a counterexample (two, in fact) to the proposition that the two expressions are equal.


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