Video Transcript
Which of the following is
true? Is it (A) root 49 is an element
of the open interval five to ∞? Is it (B) root 49 is not an
element of this open interval? Is it (C) root 49 is a subset
of this interval? Or (D) root 49 is not a subset
of this interval.
Now, when we read options (C)
and (D), we said that this means it’s a subset or not a subset of this interval,
respectively. Now, of course, for this
notation to be valid, both root 49 and the open interval from five to ∞ must be
sets. But of course, the square root
of 49 is not a set. And this means we can instantly
disregard options (C) and (D).
In order to determine which of
(A) and (B) is true, let’s look to evaluate the square root of 49. Now, this is one that we should
know by heart. The square root of 49 is equal
to seven. Then, we can note that the
lower bound of each of our intervals is five. And we know that seven is
greater than five. This in turn means that the
square root of 49 must be greater than five. But of course, it’s only
seven. It’s definitely not as big as
∞. So we can say that the square
root of 49 is greater than five and less than ∞. And that’s equivalent to saying
that the square root of 49 is an element of the open interval from five to
∞. So the correct answer is
(A).
