If x is rational and y is irrational then x + y is irrational(True or false)

Solution:

If x is rational and y is irrational then their sum is irrational. The statement is true.

Let the above fact be demonstrated:

Let x be a rational number 3 which is of the form p/q (as it can be written as 3/1).

Let y be an irrational number, say √2 .

√2 is irrational as it is not only interminable but also cannot be expressed in the form of p/q (q ≠ 0).

√2 = 1.4142135623731…….

So now if we add √2 to 3 then we have

√2 + 3 = 4.4142135623731…….

Therefore √2 + 3 is also non terminable which cannot be expressed as p/q.

If x is rational and y is irrational then x + y is irrational(True or false)

Summary:

If x is rational and y is irrational then x + y is irrational is a true statement.