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प्रश्न
Write the negation of the following statement.
Some continuous functions are differentiable.
उत्तर
All continuous functions are not differentiable.
संबंधित प्रश्न
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3 "
Write the dual of the following statements: (p ∨ q) ∧ T
Write the dual of the following statements:
Madhuri has curly hair and brown eyes.
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
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.
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) ≡ ∼ p → (p → q)
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
Using the truth table prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table proves the following logical equivalence.
∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (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)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∧ (p → q)] → q
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
Prove that the following statement pattern is a tautology.
(p ∧ q) → q
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a contradiction.
(p ∨ q) ∧ (~p ∧ ~q)
If p is any statement then (p ∨ ∼p) is a ______.
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → 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 ∨ r) ≡ (p ∨ q) ∨ r
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
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)
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
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) ∨ (p → 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
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
Construct the truth table for the following statement pattern.
(p ∧ r) → (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 ∨ r)] ↔ ~[p → (q → 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)] ∧ ~p
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
State the dual of the following statement by applying the principle of duality.
(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
State the dual of the following statement by applying the principle of duality.
2 is even number or 9 is a perfect square.
Complete the truth table.
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | `square` | T |
| T | T | F | F | `square` | `square` |
| T | F | T | T | `square` | T |
| T | F | F | T | `square` | `square` |
| F | T | T | `square` | F | T |
| F | T | F | `square` | T | `square` |
| F | F | T | `square` | F | T |
| F | F | F | `square` | T | `square` |
The given statement pattern is a `square`
If p → (∼p v q) is false, then the truth values of p and q are respectively
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Which of the following is not true for any two statements p and q?
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
