English

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.

Advertisements
Advertisements

Question

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.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is True.

Explanation:

Here, the given statement is of the form p ∧ q which has the truth value T whenever both p and q have the truth value T.

Hence, it is a true statement and its component statements are:

p: 24 is a multiple of 4.   ......(True)

q: 24 is a multiple of 6.  ......(True)

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 3.(ii) | Page 262

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Show that the statement “For any real numbers a and ba2 = b2 implies that a = b” is not true by giving a counter-example.


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

Two non-empty sets have always a non-empty intersection.


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

 Go !


Write the negation of the statement:
Banglore is the capital of Karnataka.


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:

q : For every real number x, either x > 1 or x < 1.


Find the component statement of the compound statement:

 25 is a multiple of 5 and 8.

 

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 =5.

 

Write the negation of  statement:

For every x ϵ Nx + 3 < 10


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

 It is necessary to be rich in order to be happy.


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". 

 It never rains when it is cold.

 

 statement are true and false? In each case give a valid reason for saying so

 s : If x and y are integers such that x > y, then − x < − y.


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.


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

2 is a positive number or a negative number.


Write the negation of the following statements:
x + y = y + x and 29 is a prime number.


Rewrite the following statements in the form of conditional statements:

Ramesh will get dessert only if he eats his dinner.


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


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.


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


Find the component statements of the following compound statements.

Number 7 is prime and odd.


Find the component statements of the following compound statements.

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


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.

All living things have two eyes and two legs.


Translate the following statements into symbolic form

2, 3 and 6 are factors of 12


Rewrite the following statements in the form of conditional statements

The unit digit of an integer is 0 or 5 if it is divisible by 5.


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.


Which of the following is not a statement>


The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.


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


The negation of the statement “Plants take in CO2 and give out O2 ” is ______.


The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×