Taking different numbers as x, y and compute x + y, x – y. Check whether the following hold for all kinds of numbers.

(x + y) – x = y

Let’s take x as : 1,2,3,4

And respectively y as : -1,-2,-3,-4

For x = 1 and y = -1:

(x + y) = (1 - 1) = 0

(x - y) = (1 – (-1)) = 2

For x = 2 and y = -2:

(x + y) = (2 - 2) = 0

(x - y) = (2 – (-2)) = 4

For x = 3 and y = -3:

(x + y) = (3 - 3) = 0

(x - y) = (3 – (-3)) = 6

For x = 4 and y = -4

(x + y) = (4 - 4) = 0

(x - y) = (4 – (-4)) = 8

(i) (x + y) – x = y

Let’s check for x = 1 and y = -1

L.H.S = (1 + (-1)) – 1

= (0) – 1

= -1

R.H.S = y

= -1

= L.H.S

Hence, it holds for x = 1 and y = -1

Let’s check for x = 2 and y = -2

L.H.S = (2 + (-2)) – 2

= (0) – 2

= -2

R.H.S = -2

= L.H.S

Hence, it works for x = 2 and y = -2

Similarly we can check for other values too. It will follow.