Question

Which of the following intervals are subsets of the interval $[-3,7)$

• A. $(3,7)$
• B. $(-1,7]$
• C. $(-1,7)$
• D. $(-3,-1)$

Answer 1

Answer: (A), (C), (D)

$(-3,-1)$

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 $[-3,7)$, $7$ is not included while $-3$ is included in the interval. Hence the correct options are $(3,7),(-1,7)\text{and}(-3,-1)$