**Topic**

Let \(A = \left[ {m;m + 2} \right]\) and \(B = \left[ {n;n + 1} \right]\) where m, n are actual parameters. Find the condition of the numbers m and n so that the set \(A \cap B\) contains exactly one element.

**Detailed explanation**

For the set \(A \cap B\) to contain exactly one element, then \(\left[{\begin{array}{*{20}{c}}{m+2=n}\\{n+1=m}\end{array}}\right\Leftrightarrow\left[{\begin{array}{*{20}{c}}{m=nā2}\\{m=n+1}\end{array}}\right\)[{\begin{array}{*{20}{c}}{m+2=n}\{n+1=m}\end{array}}\right\Leftrightarrow\left[{\begin{array}{*{20}{c}}{m=nā2}\{m=n+1}\end{array}}\right\)

So for \(m = n ā 2\) or \(m = n + 1\) then \(A \cap B\) contains exactly one element