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प्रश्न
Complete the truth table.
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | `square` | T |
| T | T | F | F | `square` | `square` |
| T | F | T | T | `square` | T |
| T | F | F | T | `square` | `square` |
| F | T | T | `square` | F | T |
| F | T | F | `square` | T | `square` |
| F | F | T | `square` | F | T |
| F | F | F | `square` | T | `square` |
The given statement pattern is a `square`
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उत्तर
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | T | T |
| T | T | F | F | T | T |
| T | F | T | T | T | T |
| T | F | F | T | T | T |
| F | T | T | T | F | T |
| F | T | F | F | T | T |
| F | F | T | T | F | T |
| F | F | F | T | T | T |
The given statement pattern is a tautology.
संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
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Prove that the following statement pattern is a contradiction.
(p → q) ∧ (p ∧ ~ q)
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
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~(p ∧ q) ≡ ~ p ∨ ~ q
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With proper justification, state the negation of the following.
(p → q) ∧ r
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
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(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
If p → (∼p v q) is false, then the truth values of p and q are respectively
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Write the negation of the following statement:
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Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
