3. Is the statement ~(p V q) the logical equivalent of p +q ? Use a truth table to demonstrate you answer. Skip no Columns. Evaluate the truth value of the statements. Justify your answer. a) ax[(x < 0) → (3x² < 0)] b) Vx[(x – 62 2) V (x < 1)] Write an equivalent statement in terms of or "OR" or "AND" for r +s without using the → symbol.

3. Is the statement ~(p V q) the logical equivalent of p +q ? Use a truth table to demonstrate you answer. Skip no Columns. Evaluate the truth value of the statements. Justify your answer. a) ax[(x < 0) → (3x² < 0)] b) Vx[(x – 62 2) V (x < 1)] Write an equivalent statement in terms of or "OR" or "AND" for r +s without using the → symbol.

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Description: **Transcription of Educational Text**3. Is the statement \( \sim (p \lor q) $ the logical equivalent of $ p \rightarrow q $? Use a truth table to demonstrate your answer. Skip no Columns. Evaluate the truth value of the statements. Justify your a

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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**Transcription of Educational Text**

3. Is the statement $ \sim (p \lor q) $ the logical equivalent of $ p \rightarrow q $? Use a truth table to demonstrate your answer. Skip no Columns. Evaluate the truth value of the statements. Justify your answer.

a) $\exists x[(x < 0) \rightarrow (3x^2 < 0)]$

b) $\forall x[(x - 6 \geq 2) \lor (x < 1)]$

Write an equivalent statement **in terms of** “OR” or “AND” for $ r \rightarrow s $ without using the $ \rightarrow $ symbol.

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