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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.
[(p→q) ∧ q]→p
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3 "
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
Using the truth table prove the following logical equivalence.
p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
Using the truth table prove the following logical equivalence.
[∼ (p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Using the truth table proves the following logical equivalence.
∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ ∼ q) ↔ (p → q)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]
Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p → q) ∨ (q → p)
Prepare truth tables for the following statement pattern.
(p ∧ r) → (p ∨ ~ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a contradiction.
(p → q) ∧ (p ∧ ~ q)
Show that the following statement pattern is contingency.
(p∧~q) → (~p∧~q)
Write the dual of the following:
~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
State the dual of the following statement by applying the principle of duality.
2 is even number or 9 is a perfect square.
The false statement in the following is ______.
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
The converse of contrapositive of ∼p → q is ______.
