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प्रश्न
State the dual of the following statement by applying the principle of duality.
2 is even number or 9 is a perfect square.
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उत्तर
2 is even number and 9 is a perfect square.
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संबंधित प्रश्न
State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.
By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency. (p → q) ∧ (p ∧ ~ q ).
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
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)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
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) → q
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the dual of the following:
~(p ∧ q) ≡ ~ p ∨ ~ q
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Write the converse, inverse, and contrapositive of the following statement.
If he studies, then he will go to college.
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(q ∧ r)
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
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 ∧ (~p ∨ q) ≡ p ∧ q
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
Write the converse, inverse, contrapositive of the following statement.
If I do not work hard, then I do not prosper.
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
The contrapositive of p → ~ q is ______
If p → (∼p v q) is false, then the truth values of p and q are respectively
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
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 ______.
In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .
- `bar(PR)`
- `bar(PM)`
- `bar(QM)`
