Show that ¬(𝑝 ∨ (¬𝑝 ∧ 𝑞)) and ¬𝑝 ∧ ¬𝑞 are logically equivalent by:a) Using a truth table (3 POINTS)b) Using logical equivalences
Question
Show that ¬(𝑝 ∨ (¬𝑝 ∧ 𝑞)) and ¬𝑝 ∧ ¬𝑞 are logically equivalent by:a) Using a truth table (3 POINTS)b) Using logical equivalences
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Solution 1
Sure, let's start with the truth table:
| p | q | ¬p | ¬q | ¬p ∧ q | p ∨ (¬p ∧ q) | ¬(p ∨ (¬p ∧ q)) | ¬p ∧ ¬q |
|---|---|---|---|---|---|---|---|
| T | T | F | F | F | T | F | F |
| T | F | F | T | F | T | F |
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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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