English

Identify the quantifiers and write the negation of the following statements:For all even integers x, x2 is also even.

Advertisements
Advertisements

Question

Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.

Sum
Advertisements

Solution

The quantifier is “for all” and the negation is

“There exists an even integer x such that x2 is not even”

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Solved Examples [Page 259]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Solved Examples | Q 13.(ii) | Page 259

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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 sentence are statement and are not. Justify your answer.

 Every set is a finite set.


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.

 This sentence is a statement.


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

Is the earth round?


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.

The product of (−1) and 8 is 8.

 

Write the negation of the statement:

 The earth is round.


Write the negation of the statement:

 The sun is cold.

 

 I will not go to school.


Write the negation of the statement:

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

 

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:

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


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

 To apply for a driving licence, you should have a ration card or a passport.

 

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:

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


Determine whether the compound statement are true or false:

 Delhi is in England and 2 + 2 = 4.
 


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

 t :  \[\sqrt{11}\]  is a rational number. 

 

 


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

2 is a positive number or a negative number.


Rewrite the following statements in the form of conditional statements:

When you sing, my ears hurt.


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.


Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”


Which of the following is a statement?


Which of the following sentences are statements? Justify

Every square is a rectangle.


Which of the following sentences are statements? Justify

Sum of opposite angles of a cyclic quadrilateral is 180°.


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


Find the component statements of the following compound statements.

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


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

2 is an even number and a prime number.


Translate the following statements into symbolic form

Rahul passed in Hindi and English.


Translate the following statements into symbolic form

x and y are even integers.


Write down the negation of following compound statements

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


Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.


Identify the Quantifiers in the following statements.

There exists a real number which is not a rational number.


Identify the Quantifiers in the following statements.

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


Check the validity of the following statement.
q: 131 is a multiple of 3 or 11


Which of the following is a statement?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×