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प्रश्न
Write the dual statement of the following compound statement.
Radha and Sushmita cannot read Urdu.
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उत्तर
Radha or Sushmita cannot read Urdu.
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संबंधित प्रश्न
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)
Write the dual of the following statements:
Madhuri has curly hair and brown eyes.
If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧ ∼ r ) ∧ ( ∼ q ∧ s )
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)] ∧ r ≡ r
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(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.
∼ (∼ q ∧ p) ∧ q
(p ∧ q) → r is logically equivalent to ________.
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) ∨ (q → p)
Prove that the following statement pattern is a tautology.
(p ∧ q) → q
Prove that the following statement pattern is a tautology.
(~p ∧ ~q ) → (p → q)
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
State the dual of the following statement by applying the principle of duality.
p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]
Write the dual of the following.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
The contrapositive of p → ~ q is ______
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______
The converse of contrapositive of ∼p → q is ______.
