Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 07, 2023

Use De Morgan's laws to write the negation of $\sim r \wedge(\sim q \rightarrow p)$ , where $\sim$ negates only simple statements.

STEP 1

Assumptions1. We are using De Morgan's laws to write the negation of the statement. . The given statement is $\sim r \wedge(\sim q \rightarrow p)$ .
3. The symbol $\sim$ negates only simple statements.

STEP 2

De Morgan's laws state that the negation of a conjunction is the disjunction of the negations, and the negation of a disjunction is the conjunction of the negations. In other words $\sim (A \wedge B) = \sim A \vee \sim B$ $\sim (A \vee B) = \sim A \wedge \sim B$

STEP 3

We can apply De Morgan's law to the given statement. The negation of the given statement is $\sim (\sim r \wedge(\sim q \rightarrow p))$

STEP 4

Applying De Morgan's law, we get $\sim (\sim r) \vee \sim (\sim q \rightarrow p)$

STEP 5

implify the statement. The negation of $\sim r$ is $r$ , and the negation of $\sim q \rightarrow p$ is $q \wedge \sim p$ .
$r \vee (q \wedge \sim p)$ So, the negation of $\sim r \wedge(\sim q \rightarrow p)$ is $r \vee (q \wedge \sim p)$ .

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