Question

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

i. (x + y) – x = y

ii. (x + y) – y = x

iii. (x – y) + y = x

Answer 1

If we take x = 6 and y = 2, x + y = 6 + 2 = 8

and x – y = 6 – 2 = 4

If x = -6 and y = 2, x + y = -6 + 2 = -4 and x – y

= -6 – 2 = -8

If x = 6 and y = -2, x + y = 6 + (-2) = 4

and x – y = 6 – (-2) = 8

If x = -6 and y = -2, x + y = (-6) + (-2)

= -8 and x – y = (-6) – (-2 ) = -4

i. (x + y) – x

If x = 6 and y = -2, (x + y) – x

= 8 – 6 = 2 = y

If x = -6 and y = 2, (x + y) – x

= -4 – (-6) = -4 + 6 = 2 = y

If x = 6 and y = -2, (x + y) – x

= 4 – 6 = – 2 = y

If x = -6 and y = -2, (x + y) – x

= -8 – (-6) = -8 + 6 = -2 = y

(x + y) – x = y, for all values of x and y

ii. (x + y) – y

If x = 6 and y = 2, (x + y) – y

= 8 – 2 = 6 = x

If x = -6 and y = 2, (x + y) – y

= -4 – 2 = -6 = x

If x = 6 and y = -2, (x + y) – y

= 4 – (-2) = 4 + 2 = 6 = x

If x = -6 and y = -2, (x + y) – y

= -8 – (-2) = -8 + 2 = -6 = x

(x + y) – y = x, for all values of x and y

iii. (x – y) + y

If x = 6 and y = 2, (x – y) + y

= 4 + 2 = 6 = x

If x = -6 and y = 2, (x – y) + y

= -8 + 2 = -6 = x

If x = 6 and y = -2, (x – y) + y

= 8 + (-2) = 8 – 2 = 6 = x

If x = -6 and y =- 2, (x – y) + y

= -4 + (-2) = -6 = x

(x – y) + y = x, for all values of x and y