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Chapter 3: Problem 20

Use De Morgan's laws to write a statement that is equivalent to the given statement. \(\sim(p \vee \sim q)\)

Short Answer

Expert verified
The statement equivalent to \(\sim(p \vee \sim q)\) according to De Morgan's laws is \(\sim p \wedge q\).

Step by step solution

01

Understand the symbols in the given statement

In the given logical statement \(\sim(p \vee \sim q)\), '\(\sim\)' signifies 'not', '\(\vee\)' signifies 'or' and '\(\wedge\)' signifies 'and'.
02

Apply De Morgan's law

According to De Morgan's laws, \(\sim(p \vee \sim q)\) is equivalent to \(\sim p \wedge \sim \sim q\).
03

Simplify the equivalent statement

The double negation \(\sim \sim q\) simplifies to \(q\). Thus, the final equivalent statement is \(\sim p \wedge q\).

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