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

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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 [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


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.

 The real number x is less than 2.


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

 Mathematics is difficult.


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

All real numbers are complex numbers.


Write the negation of the statement:

 The sun is cold.

 

 I will not go to school.


Are the pair of statement are negation of each other:

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


Write the negation of the statement:

 p : For every positive real number x, the number (x − 1) is also positive.

 


Find the component statement of the compound statement:

All rational numbers are real and all real numbers are complex.


Find the component statement of the compound statement:

 25 is a multiple of 5 and 8.

 

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

All rational numbers are real and all real numbers are not complex.


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.

 

Write the negation of  statement:

For every 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". 

You can access the website only if you pay a subscription fee.

 


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

 It rains only if it is cold.


Write the negation of the following statements:
x + y = y + x and 29 is a prime number.


Rewrite the following statements in the form of conditional statements:

Mohan will be a good student if he studies hard.


Rewrite the following statements in the form of conditional statements:

Ramesh will get dessert only if he eats his dinner.


Rewrite the following statements in the form of conditional statements:

A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.


Rewrite the following statements in the form of conditional statements:

A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.


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


Which of the following sentences are statements? Justify

Where is your bag?


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


Find the component statements of the following compound statements.

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


Translate the following statements into symbolic form

2, 3 and 6 are factors of 12


Translate the following statements into symbolic form

A number is either divisible by 2 or 3.


Write down the negation of following compound statements

6 is divisible by 2 and 3.


Rewrite the following statements in the form of conditional statements

The square of an odd number is odd.


Rewrite the following statements in the form of conditional statements

You will get a sweet dish after the dinner.


Identify the Quantifiers in the following statements.

For all negative integers x, x 3 is also a negative integers.


Check the validity of the following statement.
p: 125 is divisible by 5 and 7.


Which of the following is a statement?


The negation of the statement “72 is divisible by 2 and 3” is ______.


The negation of the statement “Plants take in CO2 and give out O2 ” is ______.


The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.


Which of the following statement is a conjunction?


State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?


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