हिंदी

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.

एक पंक्ति में उत्तर
Advertisements

उत्तर

∀ n ∈ N, (n2 + 2) is not odd number.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.8 [पृष्ठ २१]

APPEARS IN

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


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.


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 ∧ q) ≡ ∼ p


Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


Using the truth table prove the following logical equivalence.

(p ∨ q) → r ≡ (p → r) ∧ (q → 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) ∧ ∼ q] → ∼ p


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ 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.


Using the rules of negation, write the negation of the following:

(~p ∧ q) ∧ (~q ∨ ~r)


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


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) ∧ (q ∧ r)] ∨ (~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 ∧ (~p ∨ q) ≡ p ∧ q


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Express the truth of the following statement by the Venn diagram.

Some members of the present Indian cricket are not committed.


The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______. 


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______


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

(p ∧ q) → (q ∨ p)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×