Advertisements
Advertisements
प्रश्न
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
उत्तर
p | q | r | p→q | p→r | (p→q)∧(p→r) |
T | T | T | T | T | T |
T | T | F | T | F | F |
T | F | T | F | T | F |
T | F | F | F | F | F |
F | T | T | T | T | T |
F | T | F | T | T | T |
F | F | T | T | T | T |
F | F | F | T | T | T |
The truth values in the last column are not identical. Hence, it is contingency.
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.
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
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.
Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."
Using the truth table prove the following logical equivalence.
p → (q ∧ r) ≡ (p ∧ q) (p → r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(∼ p → q) ∧ (p ∧ r)
(p ∧ q) → r is logically equivalent to ________.
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)
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a tautology.
(~p ∧ ~q ) → (p → q)
Prove that the following statement pattern is a contradiction.
(p ∨ q) ∧ (~p ∧ ~q)
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q
Write the dual statement of the following compound statement.
Radha and Sushmita cannot read Urdu.
Write the dual statement of the following compound statement.
A number is a real number and the square of the number is non-negative.
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
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) ∧ (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) → p] ↔ [(~p) ∧ (~q)]
Write the converse, inverse, contrapositive of the following statement.
If 2 + 5 = 10, then 4 + 10 = 20.
If p → (∼p v q) is false, then the truth values of p and q are respectively
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
The equivalent form of the statement ~(p → ~ q) is ______.
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.