Question

use de morgans laws to write the negation of the following statement. q∧(p∨¬r)
the negation of the statement q∧(p∨¬r) is

Explanation:

Step1: Apply De - Morgan's law for $

eg(A\land B)$
De - Morgan's law states that $
eg(A\land B)=
eg A\lor
eg B$. Here $A = q$ and $B=(p\lor
eg r)$. So, $
eg(q\land(p\lor
eg r))=
eg q\lor
eg(p\lor
eg r)$.

Step2: Apply De - Morgan's law for $

eg(A\lor B)$
De - Morgan's law also states that $
eg(A\lor B)=
eg A\land
eg B$. For $A = p$ and $B=
eg r$, we have $
eg(p\lor
eg r)=
eg p\land
eg(
eg r)$.

Step3: Simplify $

eg(
eg r)$
By the double - negation law, $
eg(
eg r)=r$. So, $
eg(p\lor
eg r)=
eg p\land r$.

Step4: Combine the results

Substituting $
eg(p\lor
eg r)=
eg p\land r$ into $
eg q\lor
eg(p\lor
eg r)$, we get $
eg q\lor(
eg p\land r)$.

Answer:

$
eg q\lor(
eg p\land r)$