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प्रश्न
Write the negation of the following statement :
If the lines are parallel then their slopes are equal.
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उत्तर
The lines are parallel and their - slopes are not equal.
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संबंधित प्रश्न
If p : It is raining
q : It is humid
Write the following statements in symbolic form:
(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid.
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.
Using the truth table prove the following logical equivalence.
∼ (p ∨ q) ∨ (∼ p ∧ 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 ∨ r)] ↔ ∼ [p → (q → r)]
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(p ∨ q) ∧ ∼p] ∧ ∼q
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(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.
Write the dual statement of the following compound statement.
Radha and Sushmita cannot read Urdu.
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) v (~ q → ~ r)
With proper justification, state the negation of the following.
(p → q) ∧ 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.
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
