Advertisements
Advertisements
प्रश्न
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
Advertisements
उत्तर
| p | q | ∼p | ∼q |
p ∧ q |
∼p ∧ q | p ∨ ∼q | ∼p ∧ ∼q | (I) ∨ (II) ∨ (III) ∨ (IV) |
| (I) | (II) | (III) | (IV) | |||||
| T | T | F | F | T | F | T | F | T |
| T | F | F | T | F | F | T | F | T |
| F | T | T | F | F | T | F | F | T |
| F | F | T | T | F | F | T | T | T |
All the entries in the last column of the above truth table are T.
∴ (p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q) is a tautology.
APPEARS IN
संबंधित प्रश्न
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)`
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
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 v q) → r and (p → r) ∧ (q → r)
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 :
Every quadratic equation has only real roots.
Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."
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) ≡ ∼ p → (p → q)
Using the truth table prove the following logical equivalence.
[∼ (p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
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 ∨ 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 → ∼ q)
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) ∨ (∼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)
Prove that the following statement pattern is a tautology.
(p ∧ q) → q
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ (~p ∨ ~q)
Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → q]
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
Write the dual of the following:
~(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.
All the stars are shining if it is night.
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
The false statement in the following is ______.
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
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)
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)`
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
