Advertisements
Advertisements
प्रश्न
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
उत्तर
∼[(p `rightarrow` q) ∨ (p `rightarrow` r)]
∼(p `rightarrow` q) ∧ ∼(p `rightarrow` r)
(p ∧ ∼q) ∧ (p ∧ ∼r)
p ∧ (∼q ∧ ∼r)
p ∧ ∼(q ∨ r)
APPEARS IN
संबंधित प्रश्न
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Write the dual of the following statements: (p ∨ q) ∧ T
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧ ∼ r ) ∧ ( ∼ q ∧ s )
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.
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → 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 ∧ r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]
Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .
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 ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p → q) ∨ (q → p)
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prepare truth tables for the following statement pattern.
(p ∧ r) → (p ∨ ~ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(p ∧ ~ q) → (~ p ∧ ~ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
~ p → (p → ~ q)
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)
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ 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 → r) ∧ q
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(q ∧ r)
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) → p] ↔ [(~p) ∧ (~q)]
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
State the dual of the following statement by applying the principle of duality.
2 is even number or 9 is a perfect square.
The false statement in the following is ______.
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
The contrapositive of p → ~ q is ______
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`
Which of the following is not true for any two statements p and q?
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
