Home
Class 11
MATHS
Are the following pairs of statements ne...

Are the following pairs of statements negations of each other: (i) The number x is not a rational number. The number x is not an irrational number. (ii) The number x is a rational number. The number x is an irrational number.

Text Solution

AI Generated Solution

To determine whether the given pairs of statements are negations of each other, we will analyze each pair step by step. ### Part (i) 1. **Identify the statements:** - Statement 1: "The number x is not a rational number." - Statement 2: "The number x is not an irrational number." ...
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 14.3|4 Videos
  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 14.4|4 Videos
  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 14.1|2 Videos
  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|14 Videos
  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|11 Videos

Similar Questions

Explore conceptually related problems

Are the following pairs of statements are negation of each other: The number x is not a rational number. The number x is not an irrational number.

Are the following pairs of statements are negation of each other: The number x is not a rational number. The number x is an irrational number.

Write a pair of irrational numbers whose sum is irrational .

Write a pair of irrational numbers whose sum is rational .

Give examples of two irrational numbers the product of which is: a rational number (ii) an irrational number

Insert a rational number and an irrational number between 5 and 6.

Insert a rational number and an irrational number between 3 and 4.

Are the following statements true or false ? Give reasons for your answers. (i) Every whole number is a natural number. (ii) Every whole number is a rational number. (iii) Every integer is a rational number. (iv) Every rational number is a whole number.

The sum of two irrational numbers is an irrational number (True/false).

Which one of the following statement is true? (i) The sum of two irrational numbers is always an irrational number. (ii) The sum of two irrational numbers is always a rational number. (iii) The sum of two irrational numbers may be a rational number or irrational number. (iv) The sum of two irrational numbers is always an integer.