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Chapter 3: Problem 38

Write the negation of each statement. \(p \vee(q \wedge r)\)

Short Answer

Expert verified
The negation of the given statement \(p \vee(q \wedge r)\) is \(\neg p \wedge (\neg q \vee \neg r)\)

Step by step solution

01

Distributing the Negation

Use DeMorgan's Law to distribute the NOT operator across the compound statement. The negation of the statement '\(p \vee(q \wedge r)\)' will be '\(\neg (p \vee (q \wedge r))\)'.
02

Apply DeMorgan's Law

DeMorgan's Law states that the negation of a disjunction ('\(\vee\)', OR) is the conjunction ('\(\wedge\)', AND) of the negations. Simultaneously, the negation of a conjunction ('\(\wedge\)', AND) is the disjunction ('\(\vee\)', OR) of the negations. Therefore, apply DeMorgan's law to the statement generated in step 1, which will result in '\(\neg p \wedge (\neg q \vee \neg r)\)'.
03

Interpreting the Result

Now we have the negation of the original statement, which has been broken down into simpler expressions using DeMorgan's Law.

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Most popular questions from this chapter

Write an original argument in words for the contrapositive reasoning form.

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