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Write the negation of the following statement. ∀ n ∈ N, n + 1 > 0 - Mathematics and Statistics

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प्रश्न

Write the negation of the following statement.

∀ n ∈ N, n + 1 > 0

एका वाक्यात उत्तर
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उत्तर

∃ n ∈ N such that n + 1 ≤ 0.

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पाठ 1: Mathematical Logic - Exercise 1.8 [पृष्ठ २१]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Exercise 1.8 | Q 1.2 | पृष्ठ २१

संबंधित प्रश्‍न

If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )


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. 


Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


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 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, a contradiction or a contingency.

~ p → (p → ~ q)


Prove that the following statement pattern is a tautology.

(p ∧ q) → q


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


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


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.


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)


With proper justification, state the negation of the following.

(p → q) ∧ 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) → (r ∧ p)


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


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)


Examine whether the statement pattern

[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.


The equivalent form of the statement ~(p → ~ q) is ______.


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