Which of the following inequalities is always true for any real number 'a' and 'b'?
Choose the correct answer.
A) |a+b| >= |(|a|-|b|)| B) |a-b| <= |(|a|-|b|)| C) |a-b| = |(|a|-|b|)| D) |a-b| >= |(|a|-|b|)| E) |a-b| <= |a|-|b|
The answer here is D. One of the fundamental properties of absolute value is subadditivity, and this is a reverse triangle inequality, which is equivalent to subadditivity. So this means that difference of two any elements is something (some number) which is greater than or equal to the difference of the each element taken on itself separately, i.e. |a-b| &gt;= |(|a|-|b|)|
<result>D</result>
Which of the following inequalities is always true for any real number 'a' and 'b'?