Answer:
True statements are 4 and 5
Step-by-step explanation:
This s basically using set theory to evaluate line segments
The union of two(or more) sets is the set of elements that are in either or both sets.
Here is an example
If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6} then
A ∪ B = (1, 2, 3, 4, 5, 6}
Note that there cannot be any duplicates in a set
We have to treat the line segments as sets to solve this problem.
For easier explanation, I am going to view each segment as having points which I am labeling 1, 2, 3 etc.
The individual independent line segments are JL, LM, MN, and NT, basically each is a set of the points that comprise each segment
You have to visualize each of these line segments as being comprised of these points.
Note that these are distinct sets ie there is no common point when we consider the above 4 sets
Let set
JL have the points {1, 2, 3} we say JL = {1, 2, 3}
LM = {4, 5}
MN = {6, 7}
NT = {8, 9}
We see that there are no common points between each of the four sets below
1. JL ∪ MN = set of points that lie in JL or MN or both. Since JL and MN are distinct sets, the union of these two sets is s
JL U MN = {1, 2, 3} U {5, 6} = {1, 2, 3, 5, 6} . However, JM contains all the points from J to M which is {1, 2, 3, 4, 5} which is not the same as JL U MN
So Statement 1 is false
2. JL U MN = {1, 2, 3} U {6, 7} = {1, 2, 3, 6, 7} so it contains more points than MN{6, 7} and therefore Statement 2 is false
3. LM U LN
We can see that LN contains all the points in LM and MN = {4, 5, 6, 7}. LM U LN = {4, 5} U { 4, 5, 6, 7} = {4, 5, 6, 7}. But LM is only a subset of LN and has fewer points {4, 5} so Statement 3 is false
4. LM U LN
LM = {4, 5}, LN = {4, 5, 6, 7} so LM U LN = {4, 5, 6, 7} = LN. Remember sets don't duplicate. So Statement 4 is True
5. NT U JT
NT = {8, 9} and JT = set of all points in the segment from J to T which is all the points. So JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} and NT U JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} which is the set of all points in JT. Therefore Statement 5 is True
The figure below shows a graphical representation of what I wrote above. If you look at LN for instance, it has 4 points {4, 5, 6, 7} and therefore represents all the points in LM and LN (without duplication of points). This is Statement 4, by the way
