Advertisements
Advertisements
प्रश्न
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
उत्तर
| 1 | 2 | 3 | 4 | 5 | 6 |
| p | q | ~q | p→q | p→(p→q) | ~q→(p→q) |
| T | T | F | T | T | T |
| T | F | T | F | F | F |
| F | T | F | T | T | T |
| F | F | T | T | T | T |
In the above truth table, entries in columns 5 and 6 are identical.
∴ p → (p → q) ≡ ~ q → (p → q)
APPEARS IN
संबंधित प्रश्न
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Write the negation of the following statement :
If the lines are parallel then their slopes are equal.
State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.
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)] ∧ r ≡ r
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 ∧ (p → q)] → q
Prove that the following statement pattern is a tautology.
(p ∧ q) → 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)
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
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) ≡ (p ∨ q) ∨ r
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~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 ≡ [(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.
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) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
Which of the following is not true for any two statements p and q?
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
