Advertisements
Advertisements
प्रश्न
Prove that the following statement pattern is a contradiction.
(p → q) ∧ (p ∧ ~ q)
Advertisements
उत्तर
| p | q | ~q | p→q | p∧~q | (p→q)∧(p∧~q) |
| T | T | F | T | F | F |
| T | F | T | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | F | F |
All the truth values in the last column are F. Hence, it is a contradiction.
APPEARS IN
संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Write the dual of the following statements: (p ∨ q) ∧ T
Write converse and inverse of the following statement:
“If a man is a bachelor then he is unhappy.”
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
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)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ ∼ q) ↔ (p → q)
Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∧ (p → q)] → q
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 ∨ q) ∧ (~ p ∨ ~ q)
Prove that the following statement pattern is a contradiction.
(p ∨ q) ∧ (~p ∧ ~q)
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r
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, (n2 + 2) is odd number.
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
Write the converse, inverse, contrapositive of the following statement.
If 2 + 5 = 10, then 4 + 10 = 20.
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
If p → (∼p v q) is false, then the truth values of p and q are respectively
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
The converse of contrapositive of ∼p → q is ______.
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
