English

Translate the following statements into symbolic form A number is either divisible by 2 or 3.

Advertisements
Advertisements

Question

Translate the following statements into symbolic form

A number is either divisible by 2 or 3.

Sum
Advertisements

Solution

p: a number is divisible by 2.

q: a number is divisible by 3.

p ∨ q: a number divisible by 2 or 3.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Exercise [Page 263]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Exercise | Q 5.(v) | Page 263

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.


By giving a counter example, show that the following statements are not true.

p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.


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.

All real numbers are complex numbers.


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:

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


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.


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.


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.


Determine whether the compound statement are true or false: 

 Delhi is in India 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 never rains when it is cold.

 

Check the validity of the statement:

 p : 100 is a multiple of 4 and 5.


Which of the following statements are compound statements 

“Ram and Rahim are friends”


Translate the following statements in symbolic form

2 and 3 are prime numbers 


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.


Rewrite the following statements in the form of conditional statements:

Mohan will be a good student if he studies hard.


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.


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

y + 9 = 7.


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°.


Find the component statements of the following compound statements.

`sqrt(7)` is a rational number or an irrational number.


Find the component statements of the following compound statements.

A rectangle is a quadrilateral or a 5-sided polygon.


Rewrite the following statements in the form of conditional statements

The square of a prime number is not prime.


Identify the Quantifiers in the following statements.

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


Identify the Quantifiers in the following statements.

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


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 “Rajesh or Rajni lived in Bangalore” is ______.


The negation of the statement “101 is not a multiple of 3” is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×