Question

Which of the following intervals are subsets of the interval $(3,11]$

• A. $[3,4)$
• B. $(3,4)$
• C. $[9,11)$
• D. $(9,11]$

Answer 1

Answer: (B), (C), (D)

$(9,11]$

If the extreme numbers of an interval are included in the interval they are accompanied by a closed bracket i.e. $[x,y]$.
If one extreme is not included then it is accompanied by an open bracket i.e. $(x,y]$. In this case x is not included while $y$ is included in the interval.
So, we see that for the interval $(3,11]$, $3$ is not included while $11$ is included in the interval. Hence the correct options are $(3,4),[9,11)\text{and}(9,11]$