Advertisements
Advertisements
प्रश्न
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
उत्तर
Truth Table
(1) | (2) | (3) | (4) | (5) |
p | q | p ∧ q | ∼(p ∧ q) | p ∨ [∼(p ∧ q)] |
T | T | T | F | T |
T | F | F | T | T |
F | T | F | T | T |
F | F | F | T | T |
All entries in coloumn (5) are T's
p ∨ [∼(p ∧ q)] is Tautology.
APPEARS IN
संबंधित प्रश्न
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Write the dual of the following statements: (p ∨ q) ∧ T
State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.
Using the truth table prove the following logical equivalence.
p → (q → p) ≡ ∼ p → (p → q)
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
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)
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 ) → (p → q)
If p is any statement then (p ∨ ∼p) is a ______.
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 –––––––––.
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ p ∨ q
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
Write the negation of the following statement.
∀ n ∈ N, n + 1 > 0
Write the negation of the following statement.
∃ n ∈ N, (n2 + 2) is odd number.
Write the negation of the following statement.
Some continuous functions are differentiable.
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 ∧ r) → (p ∨ ~q)
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.
p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]
Write the dual of the following.
(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
Write the dual of the following.
13 is prime number and India is a democratic country
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Which of the following is not equivalent to p → q.
The equivalent form of the statement ~(p → ~ q) is ______.
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼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)
In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .
- `bar(PR)`
- `bar(PM)`
- `bar(QM)`