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प्रश्न
Write the negation of the following statement.
∃ n ∈ N, (n2 + 2) is odd number.
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उत्तर
∀ n ∈ N, (n2 + 2) is not odd number.
संबंधित प्रश्न
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
Using the truth table prove the following logical equivalence.
[∼ (p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
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
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ p ∨ q
Write the dual of the following:
~(p ∧ q) ≡ ~ p ∨ ~ q
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
Write the dual statement of the following compound statement.
A number is a real number and the square of the number is non-negative.
Write the negation of the following statement.
All the stars are shining if it is night.
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
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.
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[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
The false statement in the following is ______.
If p → (∼p v q) is false, then the truth values of p and q are respectively
Which of the following is not equivalent to p → q.
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
The converse of contrapositive of ∼p → q is ______.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
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)`
