English

Check the validity of the statements:r: 100 is a multiple of 4 and 5.

Advertisements
Advertisements

Question

Check the validity of the statements:
r: 100 is a multiple of 4 and 5.

Sum
Advertisements

Solution

Let p: r ∧ s

Where r: “100 is a multiple of 4” is true

s: “100 is a multiple of 5” is true

Hence p is true.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Solved Examples [Page 260]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Solved Examples | Q 15.(i) | Page 260

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find out the following  sentence is a statement and is not. Justify your answer.

Listen to me, Ravi !


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

 Go !


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

 The real number x is less than 2.


All birds sing.


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:

 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.

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


Determine whether the compound statement are true or false:

 Delhi is in India and 2 + 2 = 4.
 


Determine whether the compound statement are true or false:

 Delhi is in England and 2 + 2 = 4.
 


Write the negation of  statement:

 There exists x ϵ Nx + 3 = 10

 

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

 The game is cancelled only if it is raining.


Check the validity of the statement:

 p : 100 is a multiple of 4 and 5.


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

2 is a positive number or a negative number.


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.


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


Write the negation of the following statements:
q: 9 is a multiple of 4.


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


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


Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day


Which of the following sentences are statements? Justify

0 is a complex number.


Which of the following sentences are statements? Justify

Sky is red.


Which of the following sentences are statements? Justify

y + 9 = 7.


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


Find the component statements of the following compound statements.

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


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

2, 3 and 6 are factors of 12


Translate the following statements into symbolic form

A number is either divisible by 2 or 3.


Translate the following statements into symbolic form

Students can take Hindi or English as an optional paper.


Write down the negation of following compound statements

A triangle has either 3-sides or 4-sides.


Write down the negation of following compound statements

6 is divisible by 2 and 3.


Identify the Quantifiers in the following statements.

For every natural number x, x + 1 is also a natural number.


Check the validity of the following statement.
p: 125 is divisible by 5 and 7.


The negation of the statement “72 is divisible by 2 and 3” is ______.


Which of the following is the conditional p → q?


Which of the following statement is a conjunction?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×