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प्रश्न
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`
उत्तर
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | T | T |
| T | T | F | F | T | T |
| T | F | T | T | T | T |
| T | F | F | T | T | T |
| F | T | T | T | F | T |
| F | T | F | F | T | T |
| F | F | T | T | F | T |
| F | F | F | T | T | T |
The given statement pattern is a tautology.
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)
Write converse and inverse of the following statement:
“If a man is a bachelor then he is unhappy.”
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
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.
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) ∧ (p ∧ r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]
(p ∧ q) → r is logically equivalent to ________.
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) ∧ (p ∧ ∼q)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
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.
q ∨ [~ (p ∧ q)]
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
If p is any statement then (p ∨ ∼p) is a ______.
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (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 statement of the following compound statement.
Karina is very good or everybody likes her.
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
With proper justification, state the negation of the following.
(p → q) ∧ r
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
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)
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 ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ 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.
If 2 + 5 = 10, then 4 + 10 = 20.
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Write the converse, inverse, contrapositive of the following statement.
If I do not work hard, then I do not prosper.
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 dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Write the dual of the following.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
The contrapositive of p → ~ q is ______
Which of the following is not equivalent to p → q.
The equivalent form of the statement ~(p → ~ q) is ______.
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
