English

Write the Negation of the Statement: R : There Exists a Number X Such that 0 < X < 1.

Advertisements
Advertisements

Question

Write the negation of the statement:

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

 
Advertisements

Solution

 r: There exists a number x such that 0 < x < 1.
   ~r: For every real number x, either  \[x \leq 0\] or \[x < 1\] .

 

shaalaa.com
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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

Every rhombus is a square.


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

 The real number x is less than 2.


Write the negation of the statement:

 It rained on July 4, 2005.


Write the negation of the statement:

 The earth is round.


 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 x is an irrational number.


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


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

 To entry a country, you need a passport or a voter registration card.


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

 To enter into a public library children need an identity card from the school or a letter from the school authorities.


Write the negation of  statement:

 There exists x ϵ N, x + 3 = 10

 

 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.


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.


Which of the following statements are compound statements 

“2 is both an even number and a prime number”


Translate the following statements in symbolic form

Tigers are found in Gir forest or Rajaji national park.


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:

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


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 a multiple of 6 and 9.


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.


Which of the following sentences are statements? Justify

0 is a complex number.


Which of the following sentences are statements? Justify

Every set is an infinite set.


Which of the following sentences are statements? Justify

Every square is a rectangle.


Find the component statements of the following compound statements.

Plants use sunlight, water and carbon dioxide for photosynthesis.


Find the component statements of the following compound statements.

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


Write the component statements of the following compound statements and check whether the compound statement is true or false.

24 is a multiple of 4 and 6.


Translate the following statements into symbolic form

Rahul passed in Hindi and English.


Write down the negation of following compound statements

All real numbers are rationals or irrationals.


Write down the negation of following compound statements

x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.


Write down the negation of following compound statements

35 is a prime number or a composite number


Write down the negation of following compound statements

|x| is equal to either x or – x.


Identify the Quantifiers in the following statements.

There exists a triangle which is not equilateral.


Which of the following is a statement?


The negation of the statement “A circle is an ellipse” is ______.


The negation of the statement “7 is greater than 8” is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×