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Write the negation of the following statement. It is false that Nagpur is capital of Maharashtra

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प्रश्न

Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra

एका वाक्यात उत्तर
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उत्तर

Nagpur is capital of Maharashtra.

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पाठ 1: Mathematical Logic - Exercise 1.3 [पृष्ठ ७]

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संबंधित प्रश्‍न

Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Write the truth value of the negation of the following statement.

London is in England.


Write the following statement in symbolic form.

If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.


If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The Sun has set and Moon has risen.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If Kiran drives the car, then Sameer will walk.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The necessary condition for existence of a tangent to the curve of the function is continuity.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is interesting iff the proof is lengthy.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r


Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


Rewrite the following statement without using the connective ‘If ... then’.

If it rains then the principal declares a holiday.


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Write the negation of the following statement.

10 > 5 and 3 < 8


Negation of p → (p ˅ ∼ q) is ______


If p → q is an implication, then the implication ∼ q → ∼ p is called its


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


Which of the following is false?


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 


The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______


Which of the following is logically equivalent to `∼(∼p \implies q)`?


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

  1. Seema is thin and happy.
  2. If Seema is fat then she is unhappy.

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