Let's simplify the given expression step by step:
The expression is [tex]\((4-5)-(13-18+2)\)[/tex].
First, we simplify the expression inside the parentheses:
[tex]\[
13 - 18 + 2
\][/tex]
Calculate [tex]\(13 - 18\)[/tex]:
[tex]\[
13 - 18 = -5
\][/tex]
Now, add 2 to the result:
[tex]\[
-5 + 2 = -3
\][/tex]
So, the expression inside the parentheses simplifies to -3.
Next, we need to simplify the entire expression:
[tex]\[
(4 - 5) - (-3)
\][/tex]
Calculate [tex]\(4 - 5\)[/tex]:
[tex]\[
4 - 5 = -1
\][/tex]
Now, subtract [tex]\(-3\)[/tex]:
[tex]\[
-1 - (-3)
\][/tex]
Remember, subtracting a negative number is the same as adding the positive equivalent:
[tex]\[
-1 + 3 = 2
\][/tex]
Therefore, the simplified value of the given expression is [tex]\(2\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
