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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
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 )
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.
State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.
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
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) → r ≡ (p → r) ∧ (q → 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) ∧ ∼ q] → ∼ p
Prove that the following statement pattern is a tautology.
(~p ∧ ~q ) → (p → q)
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ 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.
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
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) ∨ (~p)] ∨ [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 ∧ (~p ∨ q) ≡ p ∧ q
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Using truth table verify that:
(p ∧ q)∨ ∼ 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)
