Advertisements
Advertisements
प्रश्न
Using the truth table prove the following logical equivalence.
p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
Advertisements
उत्तर
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p | q | p ↔ q | p ∨ q | p ∧ q | ∼ (p ∧ q) | (p ∨ q) ∧ ∼ (p ∧ q) | ∼ [(p ∨ q) ∧ ∼ (p ∧ q)] |
| T | T | T | T | T | F | F | T |
| T | F | F | T | F | T | T | F |
| F | T | F | T | F | T | T | F |
| F | F | T | F | F | T | F | T |
The entries in columns 3 and 8 are identical.
∴ p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
APPEARS IN
संबंधित प्रश्न
If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧ ∼ r ) ∧ ( ∼ q ∧ s )
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.
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) ∨ (∼ p ∧ q) ≡ ∼ p
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)
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)
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 → r)] ↔ [(p ∧ q) → r]
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(p ∧ ~ q) → (~ p ∧ ~ q)
Prove that the following statement pattern is a tautology.
(p ∧ q) → q
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
Show that the following statement pattern is contingency.
(p∧~q) → (~p∧~q)
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]
Write the dual of the following:
p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r
Write the dual of the following:
~(p ∧ q) ≡ ~ p ∨ ~ q
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
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
Write the converse, inverse, and contrapositive of the following statement.
If he studies, then he will go to college.
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)
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
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.
(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
Write the dual of the following.
(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
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) → (q ∨ p)
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
