हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Let p: x + y = y + x

And q: 29 is a prime number.

Then the conjunction in (ii) is given by p ∧ q.

Now ~ p: x + y ≠ y + x

And ~  q: 29 is not a prime number.

Therefore, using (D7), negation of p ∧ q is given by,

~ ( p ∧ q): x + y ≠ y + x or 29 is not a prime number.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 14: Mathematical Reasoning - Solved Examples [पृष्ठ २५७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 14 Mathematical Reasoning
Solved Examples | Q 7.(ii) | पृष्ठ २५७

वीडियो ट्यूटोरियलVIEW ALL [1]

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


Show that the statement “For any real numbers a and ba2 = b2 implies that a = b” is not true by giving a counter-example.


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

The cat pussy is black.


Write the negation of the statement:
Banglore is the capital of Karnataka.


Write the negation of the statement:

 The earth is round.


Write the negation of the statement:

 The sun is cold.

 

 Some even integers are prime.


All policemen are thieves.

 

Are the pair of statement are negation of each other:
The number is not a rational number.
The number x is not an irrational number.


Write the negation of the statement:

r : There exists a number x such that 0 < x < 1.

 

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

 It rains only if it is cold.


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

 Whenever it rains it is cold.


 statement are true and false? In each case give a valid reason for saying so

q : The centre of a circle bisects each chord of the circle.


Which of the following statements are compound statements 

“Ram and Rahim are friends”


Translate the following statements in symbolic form

2 and 3 are prime numbers 


Translate the following statements in symbolic form

Tigers are found in Gir forest or Rajaji national park.


Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4


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


Which of the following is a statement?


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


Which of the following sentences are statements? Justify

Sky is red.


Which of the following sentences are statements? Justify

Where is your bag?


Which of the following sentences are statements? Justify

Every square is a rectangle.


Find the component statements of the following compound statements.

Number 7 is prime and odd.


Find the component statements of the following compound statements.

Chennai is in India and is the capital of Tamil Nadu.


Find the component statements of the following compound statements.

The number 100 is divisible by 3, 11 and 5.


Find the component statements of the following compound statements.

0 is less than every positive integer and every negative integer.


Translate the following statements into symbolic form

Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0


Identify the Quantifiers in the following statements.

There exists a triangle which is not equilateral.


Identify the Quantifiers in the following statements.

For all real numbers x and y, xy = yx.


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 even prime number other than 2.


Which of the following is the conditional p → q?


The negation of the statement “The product of 3 and 4 is 9” is ______.


Which of the following is not a negation of “A natural number is greater than zero”?


Which of the following statement is a conjunction?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×