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Identify the quantifiers and write the negation of the following statementsThere exists a number which is equal to its square.

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प्रश्न

Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.

योग
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उत्तर

The quantifier is “there exists” and the negation is

“There does not exist a number which is equal to its square”

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अध्याय 14: Mathematical Reasoning - Solved Examples [पृष्ठ २५९]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 14 Mathematical Reasoning
Solved Examples | Q 13.(i) | पृष्ठ २५९

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संबंधित प्रश्न

Show that the statement

p: “If x is a real number such that x3 + 4= 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive


By giving a counter example, show that the following statements are not true.

q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.


Find out the following  sentence is a statement and is not. Justify your answer.

Listen to me, Ravi !


Find out the sentence are statement and are not. Justify your answer.

Two non-empty sets have always a non-empty intersection.


Find out the sentence are statement and are not. Justify your answer.

 Are all circles round?


Find out the sentence are statement and are not. Justify your answer.

 Go !


Find out the sentence are statement and are not. Justify your answer.

 Mathematics is difficult.


Write the negation of the statement:

 It rained on July 4, 2005.


 Some even integers are prime.


There is a complex number which is not a real number.


Are the pair of statement are negation of each other:

 The number x is not a rational number.
The number is an irrational number.


Find the component statement of the compound statement:
 The sky is blue and the grass is green.


Find the component statement of the compound statement:

The earth is round or the sun is cold.


Write the component statement of the compound statement and check whether the compound statement is true or false:

 x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.


Write the component statement of the compound statement and check whether the compound statement is true or false:

The sand heats up quickly in the sun and does not cool down fast at night.

 

Determine whether the compound statement are true or false:

 Delhi is in India and 2 + 2 = 4.
 


Determine whether the compound statement are true or false: 

 Delhi is in India and 2 + 2 = 5.


Write the negation of  statement:

 There exists x ϵ Nx + 3 = 10

 

Negate of the  statement :

There exists a number which is equal to its square.

 

 


Write of the statement in the form "if p, then q". 

 It is necessary to be rich in order to be happy.


Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.


Identify the component statements and the connective in the following compound statements.

It is raining or the sun is shining.


Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day


Check the validity of the statements:
r: 100 is a multiple of 4 and 5.


Check the validity of the statements:
s: 60 is a multiple of 3 or 5.


The negation of the statement “It is raining and weather is cold.” is ______.


Which of the following sentences are statements? Justify

Every square is a rectangle.


Find the component statements of the following compound statements.

`sqrt(7)` is a rational number or an irrational number.


Find the component statements of the following compound statements.

A rectangle is a quadrilateral or a 5-sided polygon.


Translate the following statements into symbolic form

Students can take Hindi or English as an optional paper.


Write down the negation of following compound statements

All prime integers are either even or odd.


Identify the Quantifiers in the following statements.

For all real numbers x with x > 3, x 2 is greater than 9.


Identify the Quantifiers in the following statements.

There exists a triangle which is not an isosceles triangle.


Identify the Quantifiers in the following statements.

There exists a real number x such that x2 + 1 = 0.


The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.


The negation of the statement “101 is not a multiple of 3” is ______.


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