English

Find the component statements of the following compound statements. 0 is less than every positive integer and every negative integer. - Mathematics

Advertisements
Advertisements

Question

Find the component statements of the following compound statements.

0 is less than every positive integer and every negative integer.

Sum
Advertisements

Solution

p: 0 is less than every positive integer.

q: 0 is less than every negative integer.

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 2.(vi) | 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.


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.


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

q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.


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

 Every set is a finite set.


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

 All triangles have three sides.


Are the pair of statement are negation of each other:

 The number x is not a rational number.
The number is an irrational number.


Write the negation of the statement:

 p : For every positive real number x, the number (x − 1) is also positive.

 


Write the negation of the statement:

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


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

A lady gives birth to a baby boy or a baby girl.


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.


Write the component statement of the compound statement and check whether the compound statement is true or false:

 x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.


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

 It rains only if it is cold.


Check the validity of the statement:

 p : 100 is a multiple of 4 and 5.


Check the validity of the statement:

 r : 60 is a multiple of 3 or 5.

 

Translate the following statements in symbolic form

Tigers are found in Gir forest or Rajaji national park.


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:
x + y = y + x and 29 is a prime number.


Rewrite the following statements in the form of conditional statements:

When you sing, my ears hurt.


Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.


Check the validity of the statements:
s: 60 is a multiple of 3 or 5.


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.

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


Write the component statements of the following compound statements and check whether the compound statement is true or false.

2 is an even number and a prime number.


Translate the following statements into symbolic form

x and y are even integers.


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

2b = a + c, if a, b and c are in A.P.


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


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.


Identify the Quantifiers in the following statements.

For all negative integers x, x 3 is also a negative integers.


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


Which of the following is a statement?


Which of the following is not a statement>


The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” 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×