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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

If p is any statement then (p ∨ ∼p) is a ______. - Mathematics and Statistics

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प्रश्न

If p is any statement then (p ∨ ∼p) is a ______.

पर्याय

  • Contingency

  • Contradiction

  • Tautology

  • None of them

MCQ
रिकाम्या जागा भरा
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उत्तर

If p is any statement then (p ∨ ∼p) is a tautology.

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३०]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 1.15 | पृष्ठ ३०

संबंधित प्रश्‍न

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]


Using the truth table prove the following logical equivalence.

p → (q → p) ≡ ∼ p → (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.

(∼ 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


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 contradiction.

(p ∨ q) ∧ (~p ∧ ~q)


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ 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 ∨ r)] ↔ ~[p → (q → r)]


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


Write the converse, inverse, contrapositive of the following statement.

If 2 + 5 = 10, then 4 + 10 = 20.


State the dual of the following statement by applying the principle of duality.

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)


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.

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


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


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)


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)` .

  1. `bar(PR)`  
  2. `bar(PM)`
  3. `bar(QM)`

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