Answer:
The expression is false
Step-by-step explanation:
Given
[tex]f - (g - h) = (f - g) - h[/tex]
Required
True or False
To determine if the expression is true or false, we need to simplify both sides of the equation
[tex]f - (g - h) = (f - g) - h[/tex]
Start by opening the bracket on the right hand side
[tex]f - (g - h) = f - g - h[/tex]
Then open the bracket on the left
[tex]f - g + h = f - g - h[/tex]
Subtract f - g from both sides
[tex]f - g - (f - g) + h = f - g - (f - g) + h[/tex]
[tex]f - g - f + g + h = f - g - f + g - h[/tex]
[tex]f - f - g + g + h = f - f - g + g - h[/tex]
[tex]h \neq -h[/tex]
Hence;
The statement is false
To further check;
Assume f = 5; g = 4 and h = 3
[tex]f - (g - h) = (f - g) - h[/tex] becomes
[tex]5 - (4 - 3) = (5 - 4) - 3[/tex]
[tex]5 - 4 + 3 = 5 - 4 - 3[/tex]
[tex]2 \neq -2[/tex]
