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प्रश्न
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
उत्तर
13 is prime number or India is a democratic country.
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संबंधित प्रश्न
Write the converse and contrapositive of the statement -
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( p ∧ ∼ r ) ∧ ( ∼ q ∧ s )
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q : It is humid
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Using the truth table prove the following logical equivalence.
p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (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 prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ 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.
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Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
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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.
∼ (∼ q ∧ p) ∧ q
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Determine whether the following statement pattern is a tautology, contradiction, or contingency:
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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) ∨ (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 → (~ p ∨ q)
Prepare truth tables for the following statement pattern.
(p ∧ r) → (p ∨ ~ q)
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(p ∧ ~ q) → (~ p ∧ ~ q)
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~ p → (p → ~ q)
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Fill in the blanks :
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Show that the following statement pattern is contingency.
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Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → q]
Using the truth table, verify.
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Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
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~(p ∧ q) and ~p ∨ ~q
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Write the negation of the following statement.
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Write the negation of the following statement.
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(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) ∧ r
Construct the truth table for the following statement pattern.
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Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
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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 ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
Write the converse, inverse, contrapositive of the following statement.
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Write the converse, inverse, contrapositive of the following statement.
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[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
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| 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`
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The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
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Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
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)`
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
