Advertisements
Advertisements
प्रश्न
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ↔ q) ∧ (p → ∼ q)
उत्तर
| p | q | ∼ q | p ↔ q | p → ∼ q | (p ↔ q) ∧ (p → ∼ q) |
| T | T | F | T | F | F |
| T | F | T | F | T | F |
| F | T | F | F | T | F |
| F | F | T | T | T | T |
The entries in the last column of the above truth table are neither all T nor all F.
∴ (p ↔ q) ∧ (p → ∼ q) is a contingency.
APPEARS IN
संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Write converse and inverse of the following statement:
“If a man is a bachelor then he is unhappy.”
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
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.
State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.
Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."
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 → p) ≡ ∼ p → (p → q)
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) → (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) ↔ (p → q)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(∼ 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)]
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 → 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)
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
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)
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)
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)
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
Write the dual statement of the following compound statement.
Radha and Sushmita cannot read Urdu.
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 → r) ∧ q
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~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) → 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 ∧ (~p ∨ q) ≡ p ∧ q
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.
2 is even number or 9 is a perfect square.
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Write the dual of the following.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)
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.
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
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)
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
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)
The converse of contrapositive 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)`
