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प्रश्न
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
उत्तर
Karina is very good and everybody likes her.
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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)
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
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:
x2 ≥ 1
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 → p) ≡ ∼ p → (p → q)
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.
(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)]
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ (~p ∨ ~q)
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Show that the following statement pattern is contingency.
(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]
Write the dual of the following:
(p ∨ q) ∨ r
Write the negation of the following statement.
∀ n ∈ N, n + 1 > 0
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
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)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
State the dual of the following statement by applying the principle of duality.
2 is even number or 9 is a perfect square.
Write the dual of the following.
(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
