हिंदी

Identify the Quantifiers in the following statements. For all negative integers x, x 3 is also a negative integers. - Mathematics

Advertisements
Advertisements

प्रश्न

Identify the Quantifiers in the following statements.

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

योग
Advertisements

उत्तर

Quantifier means a phrase like ‘there exists’, ‘for all’ and ‘for every’ etc.

For all

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 14: Mathematical Reasoning - Exercise [पृष्ठ २६४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 14 Mathematical Reasoning
Exercise | Q 11.(vii) | पृष्ठ २६४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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.

All real numbers are complex numbers.


Give three examples of sentences which are not statements. Give reasons for the answers.


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


 Both the diagonals of a rectangle have the same length.


Write the negation of the statement:

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

 


Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
 There exist real numbers a and b for which a + b = b + a.


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

A lady gives birth to a baby boy or a baby girl.


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". 

 The game is cancelled only if it is raining.


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

 Whenever it rains it is cold.


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”


Which of the following statements are compound statements 

“9 is neither an even number nor a prime number”


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

It is raining or the sun is shining.


Write the truth value of the following statements.
(i) 9 is an even integer or 9 + 1 is even.
(ii) 2 + 4 = 6 or 2 + 4 = 7
(iii) Delhi is the capital of India and Islamabad is the capital of Pakistan.
(iv) Every rectangle is a square and every square is a rectangle
(v) The sun is a star or sun is a planet.


Write the negation of the following statements:
p: All triangles are equilateral triangles.


Write the negation of the following statements:
Suresh lives in Bhopal or he lives in Mumbai.


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


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


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


Identify the quantifiers and write the negation of the following statements:
There exists a number which is a multiple of 6 and 9.


Which of the following is a statement?


Which of the following sentences are statements? Justify

15 + 8 > 23


Which of the following sentences are statements? Justify

Where is your bag?


Find the component statements of the following compound statements.

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


Find the component statements of the following compound statements.

Two lines in a plane either intersect at one point or they are parallel.


Translate the following statements into symbolic form

A number is either divisible by 2 or 3.


Translate the following statements into symbolic form

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


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.


Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.


Identify the Quantifiers in the following statements.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×