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Discrete Math Logic Mathematics

Tan K.

asked • 03/09/21

Please help me answer thanks!!

Find the negation of the following statement:

~p -> (~q ^ ~p)

and simplify your answer to the simplest form.

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1 Expert Answer

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Pasquale D. answered • 03/12/21

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We want: $\sim(\sim p \Rightarrow (\sim q \wedge \sim p))$ . Our "larger" expression is a conditional, and conditionals are negated as $P \wedge \sim Q$ . Thus,

$\sim(\sim p \Rightarrow (\sim q \wedge \sim p)) \equiv \sim p \wedge \sim(\sim q \wedge \sim p).$

Now we need: $\sim(\sim q \wedge \sim p)$ . Conjunctions are negated as: $\sim P \vee \sim Q$ . Hence,

$\sim p \wedge \sim(\sim q \wedge \sim p) \equiv \sim p \wedge q \vee p.$

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