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प्रश्न
Write the negation of the following statement.
Some continuous functions are differentiable.
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उत्तर
All continuous functions are not differentiable.
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 "
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."
Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
Write the negation of the following statement :
If the lines are parallel then their slopes are equal.
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) → (q ∨ p)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
∼ (∼ q ∧ p) ∧ q
Prove that the following statement pattern is a tautology.
(p ∧ q) → q
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → q]
Write the dual of the following:
(p ∨ q) ∨ r
Write the dual of the following:
~(p ∧ q) ≡ ~ p ∨ ~ q
Write the dual statement of the following compound statement.
A number is a real number and the square of the number is non-negative.
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
Write the converse, inverse, and contrapositive of the following statement.
If he studies, then he will go to college.
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
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.
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[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.
p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
The contrapositive of p → ~ q is ______
Which of the following is not true for any two statements p and q?
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)`
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
