1
Question
Write the negation of: p↔(q∨r)
Write the negation of: p↔(q∨r)
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Solution
The correct option is D (p∧∼q∧∼r)∨(q∨r∧∼p)
p q r ∼p ∼q ∼r p∧∼q p∧∼q∧∼r q∨r q∨r∧∼p (p∧∼q∧∼r)∨(q∨r∧∼p) T T T F F F F F T F F T T F F F T F F T F F T F T F T F T F T F F T F F F T T T T F F T F T T T F F F F T T T F T F T F T F F T T T F F T T T F F F T T T F F F T T T F F F F F
p q r q∨r p↔(q∨r) ∼[p↔(q∨r)] T T T T
T F T T F T T T T F T T T F T F F F F T F T T T F T F T F T F T F F T T F T F F F F T F
Here, T=True and F=FalseNow,∴∼p↔(q∨r) is (p∧∼q∧∼r)∨(q∨r∧∼p)
| p | q | r | ∼p | ∼q | ∼r | p∧∼q | p∧∼q∧∼r | q∨r | q∨r∧∼p | (p∧∼q∧∼r)∨(q∨r∧∼p) |
| T | T | T | F | F | F | F | F | T | F | F |
| T | T | F | F | F | T | F | F | T | F | F |
| T | F | T | F | T | F | T | F | T | F | F |
| T | F | F | F | T | T | T | T | F | F | T |
| F | T | T | T | F | F | F | F | T | T | T |
| F | T | F | T | F | T | F | F | T | T | T |
| F | F | T | T | T | F | F | F | T | T | T |
| F | F | F | T | T | T | F | F | F | F | F |
| p | q | r | q∨r | p↔(q∨r) | ∼[p↔(q∨r)] |
| T | T | T | T | T | F |
| T | T | F | T | T | T |
| T | F | T | T | T | F |
| T | F | F | F | F | T |
| F | T | T | T | F | T |
| F | T | F | T | F | T |
| F | F | T | T | F | T |
| F | F | F | F | T | F |
Now,
∴∼p↔(q∨r) is
(p∧∼q∧∼r)∨(q∨r∧∼p)
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