Advertisements
Advertisements
प्रश्न
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
उत्तर
| p | q | ~p | ~q | ~p∨q | ~p∧~q | (~p∨q)∧(~p∧~q) |
| T | T | F | F | T | F | F |
| T | F | F | T | F | F | F |
| F | T | T | F | T | F | F |
| F | F | T | T | T | T | T |
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 the dual of the following statements:
Madhuri has curly hair and brown eyes.
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
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.
By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency. (p → q) ∧ (p ∧ ~ q ).
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)
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 ∨ r)] ↔ ∼ [p → (q → r)]
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)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(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)
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 –––––––––.
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q
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.
Some continuous functions are differentiable.
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(q ∧ r)
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)
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Write the converse, inverse, contrapositive of the following statement.
If I do not work hard, then I do not prosper.
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
The false statement in the following is ______.
Write the dual of the following.
13 is prime number and India is a democratic country
Which of the following is not equivalent to p → q.
Which of the following is not true for any two statements p and q?
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
