## Solution 38 Page 15 Math Workbook 10 – Kite>

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 $$\left[{\begin{array}{*{20}{c}}{m+2=n}\\{n+1=m}\end{array}}\right\Leftrightarrow\left[{\begin{array}{*{20}{c}}{m=n–2}\\{m=n+1}\end{array}}\right$$[{\begin{array}{*{20}{c}}{m+2=n}\{n+1=m}\end{array}}\right\Leftrightarrow\left[{\begin{array}{*{20}{c}}{m=n–2}\{m=n+1}\end{array}}\right\)

So for $$m = n – 2$$ or $$m = n + 1$$ then $$A \cap B$$ contains exactly one element