State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0,0)
Answers
( i) infinite set
( ii) finite set
( iii) infinite set
(iv ) finite set
(v) infinite set
I hope answer was helpful
Step-by-step explanation:
(i) The set of lines that are parallel to the x-axis is
an inifinite set
. The lines parallel to the x-axis has the formula of
y
=
k
where
k
is any real number. Since there are an infinite number of real numbers, then the set of line parallel to the x-axis is an infinite set.
(ii) The set of letters in the English alphabet is
a finite set
.
There is a final element in the English alphabet and there are only
26
letters, makng it not only countable but also finite.
(iii) The set of numbers where are multiples of
5
are
an infinite set
.
There are infinite real numbers and as such there are also an inifinte number of multiples of
5
.
(iv) The set of animals living on Earth is
a finite set
.
This number is incredibly large and a physically large task but that does not mean that there is no end to the number of animals on earth at any given time. The earth has boundaries and has a fixed area and this also limits the places where animals can live, makit this a finite set.
(v) The set of circles passing through the origin
(
0
,
0
)
is
an infinite set
.
The equation of a circle is
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
where
(
h
,
k
)
is the coordinates of the center of the circle and
r
is its radius. These constants,
h
,
k
and
r
, are all real numbers and since there are an infinite number of real numbers, the there are an infinite number of lines that passes the origin.