English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

p ↔ q: A natural number is odd if and only if it is not divisible by 2.

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

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 11
Chapter 14 Mathematical Reasoning
Exercise | Q 8.(ii) | Page 263

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.

Every rhombus is a square.


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

Is the earth round?


Write the negation of the statement:

 It rained on July 4, 2005.


 Both the diagonals of a rectangle have the same length.


All policemen are thieves.

 

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:

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.


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.


Determine whether the compound statement are true or false: 

 Delhi is in India and 2 + 2 = 5.


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". 

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


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

 It never rains when it is cold.

 

Check the validity of the statement:

 r : 60 is a multiple of 3 or 5.

 

 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.


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

It is raining or the sun is shining.


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

Tigers are found in Gir forest or Rajaji national park.


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


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


Write the negation of the following statements:
r: A triangle has four sides.


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


Which of the following sentences are statements? Justify

Sky is red.


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.

Plants use sunlight, water and carbon dioxide for photosynthesis.


Translate the following statements into symbolic form

Either x or x + 1 is an odd integer.


Write down the negation of following compound statements

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


Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.


Identify the Quantifiers in the following statements.

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


The negation of the statement “7 is greater than 8” is ______.


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


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 ______.


Which of the following is the conditional p → q?


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


Which of the following statement is a conjunction?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×