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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
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3 "
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)]
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Using the truth table, verify.
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∀ n ∈ N, n + 1 > 0
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
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)
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.
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) ∧ ~(q ∧ ~p)
The false statement in the following is ______.
Write the dual of the following.
13 is prime number and India is a democratic country
If p → (∼p v q) is false, then the truth values of p and q are respectively
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
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Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
