Advertisements
Advertisements
Question
If p is any statement then (p ∨ ∼p) is a ______.
Options
Contingency
Contradiction
Tautology
None of them
Solution
If p is any statement then (p ∨ ∼p) is a tautology.
APPEARS IN
RELATED QUESTIONS
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
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."
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
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)
(p ∧ q) → r is logically equivalent to ________.
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 ∧ r) → (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 ∧ ~ q) → (~ p ∧ ~ q)
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
Show that the following statement pattern is contingency.
(p∧~q) → (~p∧~q)
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
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 → r) ∧ q
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
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 ∧ (~p ∨ q) ≡ p ∧ q
State the dual of the following statement by applying the principle of duality.
(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
Write the dual of the following.
(~p ∧ q) ∨ (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.
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
The equivalent form of the statement ~(p → ~ q) is ______.
Which of the following is not true for any two statements p and q?
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
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)`