Let Q R be the set of all rational numbers Show that the set

Let Q R be the set of all rational numbers. Show that the set {sin x + cos x + 1: x element Q} has Lebesgue measure zero.

Solution

Ans-

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.