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प्रश्न
Write the dual of the following statements:
Madhuri has curly hair and brown eyes.
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उत्तर
Dual of Madhuri has curly hair and brown eyes is “Madhuri has curly hair or brown eyes”.
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संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
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)]
Using the truth table prove the following logical equivalence.
∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p
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 ∨ r) ≡ (p ∧ q) ∨ (p ∧ 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) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
~ p → (p → ~ q)
Prove that the following statement pattern is a tautology.
(~p ∧ ~q ) → (p → q)
Prove that the following statement pattern is a tautology.
(~ p ∨ ~ q) ↔ ~ (p ∧ q)
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → q]
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the dual of the following:
p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
Write the negation of the following statement.
Some continuous functions are differentiable.
Using the rules of negation, write the negation of the following:
(p → r) ∧ q
With proper justification, state the negation of the following.
(p → q) ∧ r
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
The false statement in the following is ______.
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
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`
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
