Advertisements
Advertisements
प्रश्न
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ ∼ q) ↔ (p → q)
Advertisements
उत्तर
| p | q | ∼ q | p ∧ ∼ q | p → q | (p ∧ ∼ q) ↔ (p → q) |
| T | T | F | F | T | F |
| T | F | T | T | F | F |
| F | T | F | F | T | F |
| F | F | T | F | T | F |
All the entries in the last column of the above truth table are F.
∴ (p ∧ ∼ q) ↔ (p → q) is a contradiction.
[Note: Answer in the textbook is incorrect]
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 "
Write the dual of the following statements: (p ∨ q) ∧ T
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
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.
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 → p) ≡ ∼ p → (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)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
∼ (∼ q ∧ p) ∧ q
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[p → (∼ q ∨ r)] ↔ ∼ [p → (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 ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
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 → (~ p ∨ q)
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 ) → (p → 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 ∧ ~ q)
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
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) ∨ 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 negation of the following statement.
All the stars are shining if it is night.
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)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)
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)]
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
The contrapositive of p → ~ q is ______
Write the dual of the following.
13 is prime number and India is a democratic country
If p → (∼p v q) is false, then the truth values of p and q are respectively
The equivalent form of the statement ~(p → ~ q) is ______.
Which of the following is not true for any two statements p and q?
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
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 ______
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)`
