Question

Is it true that ƒ −(g − h) = (ƒ − g) − h? Explain why you believe the equation is true or provide a counterexample to show that it is not.

Answer 1

The expression is false

Explanation:

Given

`f - (g - h) = (f - g) - h`

Required

True or False

To determine if the expression is true or false, we need to simplify both sides of the equation

`f - (g - h) = (f - g) - h`

Start by opening the bracket on the right hand side

`f - (g - h) = f - g - h`

Then open the bracket on the left

`f - g + h = f - g - h`

Subtract f - g from both sides

`f - g - (f - g) + h = f - g - (f - g) + h`

`f - g - f + g + h = f - g - f + g - h`

`f - f - g + g + h = f - f - g + g - h`

`h \\eq -h`

Hence;

The statement is false

To further check;

Assume f = 5; g = 4 and h = 3

`f - (g - h) = (f - g) - h` becomes

`5 - (4 - 3) = (5 - 4) - 3`

`5 - 4 + 3 = 5 - 4 - 3`

`2 \\eq -2`