English

Write down the negation of following compound statements 35 is a prime number or a composite number - Mathematics

Advertisements
Advertisements

Question

Write down the negation of following compound statements

35 is a prime number or a composite number

Sum
Advertisements

Solution

p: 35 is a prime number.

q: 35 is a composite number.

The negation of the above statements is

~ (p ∨ q) = (~ p ∧ ~ q): 35 is not a prime number and it is not a composite number.

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 6.(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.

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


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.


There is a complex number which is not a real number.


Write the negation of the statement:

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


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:

The earth is round or the sun is cold.


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

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


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

 p : Each radius of a circle is a chord of the circle.


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

It is raining or the sun is shining.


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.


Rewrite the following statements in the form of conditional statements:

Ramesh will get dessert only if he eats his dinner.


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.


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

A triangle has three sides.


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

15 + 8 > 23


Which of the following sentences are statements? Justify

Where is your bag?


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.

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

x and y are even integers.


Identify the Quantifiers in the following statements.

For all real numbers x and y, xy = yx.


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 triangle which is not an isosceles triangle.


Identify the Quantifiers in the following statements.

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


Identify the Quantifiers in the following statements.

There exists a real number x such that x2 + 1 = 0.


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 “Plants take in CO2 and give out O2 ” is ______.


Which of the following is not a negation of “A natural number is greater than zero”?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×