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प्रश्न
Write the dual of the following.
13 is prime number and India is a democratic country
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उत्तर
13 is prime number or India is a democratic country.
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संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Write converse and inverse of the following statement:
“If a man is a bachelor then he is unhappy.”
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)]
Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ 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.
(∼ 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) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
~(p ∧ q) ≡ ~ p ∨ ~ q
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(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 ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
