Advertisements
Advertisements
प्रश्न
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Advertisements
उत्तर
(p ∧ q) ∨ ~ r
| p | q | r | ~r | p ∧ q | (p ∧ q) ∨ ~ r |
| T | T | T | F | T | T |
| T | T | F | T | T | T |
| T | F | T | F | F | F |
| T | F | F | T | F | T |
| F | T | T | F | F | F |
| F | T | F | T | F | T |
| F | F | T | F | F | F |
| F | F | F | T | F | T |
APPEARS IN
संबंधित प्रश्न
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3 "
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:
Madhuri has curly hair and brown eyes.
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 a tautology : ( q → p ) v ( p → q )
If p : It is raining
q : It is humid
Write the following statements in symbolic form:
(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid.
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
Write the negation of the following statement :
If the lines are parallel then their slopes are equal.
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
Using the truth table prove the following logical equivalence.
p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
Using the truth table proves the following logical equivalence.
∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)
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.
∼ (∼ q ∧ p) ∧ q
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 ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
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 ∧ q)]
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
~ p → (p → ~ q)
Prove that the following statement pattern is a tautology.
(p ∧ q) → 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)
Show that the following statement pattern is contingency.
(p∧~q) → (~p∧~q)
Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → q]
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
(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.
Radha and Sushmita cannot read Urdu.
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 negation of the following statement.
∃ n ∈ N, (n2 + 2) is odd number.
Using the rules of negation, write the negation of the following:
(p → r) ∧ q
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
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 ∨ r)] ↔ ~[p → (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) ∨ (p ∨ q)] ∧ r ≡ r
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(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.
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 ∨ 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
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
The false statement in the following is ______.
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
The contrapositive of p → ~ q is ______
Complete the truth table.
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | `square` | T |
| T | T | F | F | `square` | `square` |
| T | F | T | T | `square` | T |
| T | F | F | T | `square` | `square` |
| F | T | T | `square` | F | T |
| F | T | F | `square` | T | `square` |
| F | F | T | `square` | F | T |
| F | F | F | `square` | T | `square` |
The given statement pattern is a `square`
Which of the following is not equivalent to p → q.
The equivalent form of the statement ~(p → ~ q) is ______.
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
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)`
