Advertisements
Advertisements
प्रश्न
State the dual of the following statement by applying the principle of duality.
p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]
उत्तर
p ∧ (q ∧ r) ≡ ~[(p ∨ q) ∧ (r ∧ s)]
APPEARS IN
संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
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.
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
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) ≡ ∼ p → (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) ∧ (p → ∼ q)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the dual of the following:
(p ∨ q) ∨ r
Write the dual of the following:
~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]
Write the dual of the following:
p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r
Write the dual of the following:
~(p ∧ q) ≡ ~ p ∨ ~ q
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
Write the negation of the following statement.
All the stars are shining if it is night.
Write the negation of the following statement.
∀ n ∈ N, n + 1 > 0
Write the negation of the following statement.
∃ n ∈ N, (n2 + 2) is odd number.
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(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) ∧ (q ∧ r)] ∨ (~q)
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.
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
The contrapositive of p → ~ q is ______
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
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`
The equivalent form of the statement ~(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)`