If x is a positive integer and y is a negative integer, then x + y is a rational number.

Yes, when you add a positive integer x to a negative integer y, the result is indeed a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the numerator p is an integer, and the denominator q is a non-zero integer. Since both x and y are integers (positive and negative, respectively), their sum x + y is also an integer, because the set of integers is closed under addition. Since any integer z can be expressed as the fraction z/1, where z is the integer and 1 is the denominator, it follows that the sum x + y, which is also an integer, can be represented as a fraction (x + y)/1. Therefore, x + y is a rational number.

If x is a positive integer and y is a negative integer, then x + y is a rational number.

= X + Y = 5 - 2 = 3

= x - Y = 5 - (-2) = 5 + 2 = 7

..(X + Y) (X - Y)

Taking Another Example :

Let X = 2 & Y = - 8

= X + Y = 2 & Y = - 8

= X - Y = 2 - (- 8) = 2 + 8 = 10

= - 6 < 10

= ( X + Y ) < ( X - Y )