Question

for x,y belong to r ,define a ration s by x s y if and only x-y+√3 is an irrational number,then s is ​

Answer 1

Answer:

Step-by-step explanation:

For every value of x belongs to R,

x-x + 2–√i.e. 2–√is an irrational number.

Therefore, it is reflexive.

Now let’s say x = 2–√ and y = 2 then, x - y + 2–√=22–√−2

which is irrational but when y = 2–√and x = 2, x - y + 2–√is not irrational therefore, it is not symmetric.

Let x - y + 2–√is irrational, and y - z + 2–√is irrational , then

In the above case, let x = 1, y = 2–√∗2and z = 2–√

Then , x - z + 2–√is not irrational , therefore, the above relation is not transitive.