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

Write the negation of the following statement. ∃ n ∈ N, (n2 + 2) is odd number. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the negation of the following statement.

∃ n ∈ N, (n2 + 2) is odd number.

एका वाक्यात उत्तर
Advertisements

उत्तर

∀ n ∈ N, (n2 + 2) is not odd number.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.8 [पृष्ठ २१]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Exercise 1.8 | Q 1.3 | पृष्ठ २१

संबंधित प्रश्‍न

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 ∨ q)] ∧ r ≡ r


Prove that the following statement pattern is a tautology.

(p ∧ q) → 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


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


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.

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


Construct the truth table for the following statement pattern.

(p ∧ r) → (p ∨ ~q)


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.


Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]


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) ∧ r ≡ p ∧ (q ∧ r)


The false statement in the following is ______.


If p → (∼p v q) is false, then the truth values of p and q are respectively


Which of the following is not equivalent to 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)


The converse of contrapositive 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)` .

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

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×