English

Find the component statements of the following compound statements. The number 100 is divisible by 3, 11 and 5. - Mathematics

Advertisements
Advertisements

Question

Find the component statements of the following compound statements.

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

Sum
Advertisements

Solution

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Exercise [Page 262]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Exercise | Q 2.(iii) | Page 262

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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

The cat pussy is black.


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

 x2 + 5 | x | + 6 = 0 has no real roots.


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

 The real number x is less than 2.


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


Write the negation of the statement:

 The earth is round.


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:

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.

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


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:

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


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.
 


Determine whether the compound statement are true or false: 

Delhi is in England and 2 + 2 =5.

 

Write the negation of  statement:

For every x ϵ Nx + 3 < 10


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". 

 Whenever it rains it is cold.


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

2 is a positive number or a negative number.


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 negation of the statement
“Everyone who lives in India is an Indian”


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.


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


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


Which of the following sentences are statements? Justify

0 is a complex number.


Which of the following sentences are statements? Justify

15 + 8 > 23


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


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

57 is divisible by 2 or 3.


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.


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.


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


Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.


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 with x > 3, x 2 is greater than 9.


Identify the Quantifiers in the following statements.

There exists a statement in above statements which is not true.


Which of the following is a statement?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×