Advertisements
Advertisements
प्रश्न
Prove that the following statement pattern is a contradiction.
(p ∨ q) ∧ (~p ∧ ~q)
Advertisements
उत्तर
| p | q | ~p | ~q | p∨q | ~p∧~q | (p∨q)∧(~p∧~q) |
| T | T | F | F | T | F | F |
| T | F | F | T | T | F | F |
| F | T | T | F | T | F | F |
| F | F | T | T | F | T | F |
All the truth values in the last column are F. Hence, it is a contradiction.
APPEARS IN
संबंधित प्रश्न
Write converse and inverse of the following statement:
“If a man is a bachelor then he is unhappy.”
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
Using the truth table prove the following logical equivalence.
∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p
(p ∧ q) → r is logically equivalent to ________.
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Prepare truth tables for the following statement pattern.
(p ∧ r) → (p ∨ ~ q)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Prove that the following statement pattern is a tautology.
(~p ∧ ~q ) → (p → q)
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
(p ∨ q) ∨ r
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.
Some continuous functions are differentiable.
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
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Write the dual of the following.
(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
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 equivalent to p → q.
Which of the following is not true for any two statements p and q?
If p → q is true and p ∧ q is false, then the truth value 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)`
