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

Answer:

The expression is false

Step-by-step 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

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

$f - g - f + g + h = f - g - f + g - h$

$f - f - g + g + h = f - f - g + g - h$

$h \neq -h$

Hence;

The statement is false

To further check;

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

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

$5 - (4 - 3) = (5 - 4) - 3$

$5 - 4 + 3 = 5 - 4 - 3$

$2 \neq -2$