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Question
Write the negation of (p∧q)→(¬p∨r)
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Solution
p q r ∼p p∧q ∼p∨r (p∧q)→(∼p∨r)=a ∼a T T T F T T T F T T F F T F F T T F T F F T T F T F F F F F T F F T T T F T T F F T F T F T T F F F T T F T T F F F F T F T T F
From the above truth table, we can find the negation of (p∧q)→(∼p∨r)
| p | q | r | ∼p | p∧q | ∼p∨r | (p∧q)→(∼p∨r)=a | ∼a |
| T | T | T | F | T | T | T | F |
| T | T | F | F | T | F | F | T |
| T | F | T | F | F | T | T | F |
| T | F | F | F | F | F | T | F |
| F | T | T | T | F | T | T | F |
| F | T | F | T | F | T | T | F |
| F | F | T | T | F | T | T | F |
| F | F | F | T | F | T | T | F |
From the above truth table, we can find the negation of (p∧q)→(∼p∨r)
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