Use Theorem 1.1.1 below to verify the logical equivalence and supply a reason for each step?

Question

I have question about Simplifying Statement Forms, this question

$$\lnot(p \lor \lnot q) \lor(\lnot p \land \lnot q) ≡ \lnot p$$

and this my answer $$\begin{align} \lnot(p \lor \lnot q) \lor(\lnot p \land \lnot q) &≡ (\lnot p \land \lnot\lnot q) \lor (\lnot p \land \lnot q)&&\text{De Morgan’s laws}\\ &≡(\lnot p \land q) \lor (\lnot p \land \lnot q)&&\text{Double Negative law}\\ &≡p \land (q \lor \lnot q) &&\text{Distributive laws}\\ &≡p \land t &&\text{Negation laws}\\ &≡p &&\text{Identity laws}\\ \end{align}$$

my answer is correct or not ?

There is just a typo when you apply the distributive law: you get $\lnot p \land (q \lor \lnot q)$. You keep $\lnot p$ in the next lines. — Taroccoesbrocco, Oct 01 '18 at 11:51

score 2 · Accepted Answer · answered Oct 01 '18 at 11:43

2

Welcome to MSE! No, its not correct. The third line should be $\neg p \wedge (q\vee \neg q)$.

answered Oct 01 '18 at 11:43

Wuestenfux

20,964

just three line? , oke thank you for you correction – Devo Avidianto P Oct 01 '18 at 11:48

Use Theorem 1.1.1 below to verify the logical equivalence and supply a reason for each step?

1 Answers1