हिंदी

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

Advertisements
Advertisements

प्रश्न

Write the negation of the following statement.

∀ n ∈ N, n + 1 > 0

एक पंक्ति में उत्तर

उत्तर

∃ n ∈ N such that n + 1 ≤ 0.

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] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.8 | Q 1.2 | पृष्ठ २१

संबंधित प्रश्न

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”


Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`


Write the dual of the following statements: (p ∨ q) ∧ T


Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )


Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."


Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1


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) ≡ ∼ p → (p → q)


Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .


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

[p → (q → r)] ↔ [(p ∧ q) → r]


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

(p → q) ∨ (q → p)


Prepare truth table for (p ˄ q) ˅ ~ r

(p ∧ q) ∨ ~ r


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 ∧ ~q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q


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 ∧ ~ r)]


Write the negation of the following statement.

Some continuous functions are differentiable.


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

(p → r) ∧ q


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)


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

[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]


Using the truth table, prove the following logical equivalence.

~p ∧ q ≡ [(p ∨ q)] ∧ ~p


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 ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


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

Some members of the present Indian cricket are not committed.


Write the dual of the following

(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)


Complete the truth table.

p q r q → r r → p (q → r) ˅ (r → p)
T T T T `square` T
T T F F `square` `square`
T F T T `square` T
T F F T `square` `square`
F T T `square` F T
F T F `square` T `square`
F F T `square` F T
F F F `square` T `square`

The given statement pattern is a `square`


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


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


The converse of contrapositive of ∼p → q is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×