Advertisements
Advertisements
प्रश्न
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
Advertisements
उत्तर
| p | q | r | ~q | ~q∨r | q→r | p→(q→r) | p→(~q∨r) | ~[p→(q→r)] | [p→(~q∨r)]↔~[p → (q → r)] |
| T | T | T | F | T | T | T | T | F | F |
| T | T | F | F | F | F | F | F | T | F |
| T | F | T | T | T | T | T | T | F | F |
| T | F | F | T | T | T | T | T | F | F |
| F | T | T | F | T | T | T | T | F | F |
| F | T | F | F | F | F | T | T | F | F |
| F | F | T | T | T | T | T | T | F | F |
| F | F | F | T | T | T | T | T | F | F |
All the truth values in the last column are F. Hence, it is contradiction.
APPEARS IN
संबंधित प्रश्न
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
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)
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 ∨ q) ∧ (~ p ∨ ~ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
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)
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) ≡ (p ∨ q) ∨ r
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
State the dual of the following statement by applying the principle of duality.
(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
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)
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
The equivalent form of the statement ~(p → ~ q) is ______.
Which of the following is not true for any two statements p and q?
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)
The converse of contrapositive of ∼p → q is ______.
