Sets

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MDBFS

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I am trying to determine if these sets are open, closed or compact.
Part a. is very simple however my problem arises in part b, c, and d.
Any advice is appreciated, specifically on how to plot these sets, once I understand how they look plotted I can easily determine it's boundary points etc
 

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This is how I went about doing part a.
Any constructive critisim is appreciated
 
We need to see your work to know what help you need.
Can you draw the defined regions.
 
I am not familiar with N( (0,3), 4). Can you please define it for me?
 
Jomo said:
I am not familiar with N( (0,3), 4). Can you please define it for me?
Click to expand...
Jomo said:
(0,7) is a set of an infinite number of points. Are all those points boundary points? Can you define a boundary point?
Click to expand...
A point let's call it 'x' is a boundary point of S if every neighbourhood of x contains at least one point from S and one point not in S.Hence in this case 0 and 7 are boundary points of the finite set S

I too am not familiar with the annotation N((0,3), 4), all I know about it is that N standard for natural numbers I assume this set is an element of the natural number line but I'm not sure of how to plot it.
 
You are correct about the boundary points being 0 and 7 and NOT (0,7). You can write that the set of boundary points are {0, 7}.
N((0,3), 4)--> (0,3) is not a natural number!
Some set theory expert will come along soon and either explain what N((0,3), 4) means or say that it is meaningless.
Meanwhile, do you see the definite of something like N((0,3), 4) in your text book?
 
Jomo said:
You are correct about the boundary points being 0 and 7 and NOT (0,7). You can write that the set of boundary points are {0, 7}.
N((0,3), 4)--> (0,3) is not a natural number!
Some set theory expert will come along soon and either explain what N((0,3), 4) means or say that it is meaningless.
Meanwhile, do you see the definite of something like N((0,3), 4) in your text book?
Click to expand...
Thank you for the clarification man, really appreciate it!

I don't see any definition for a set along that line in my textbook.
I am going to try something for that one and send it to you, if you're able to provide feedback I'll greatly appreciate that
 
No! There are two variables so you are in the x-y plane. Since x>0 and y>0, that puts you in quadrant 1. Now, in quadrant 1, draw the inequality x<y

The key to see that you are in the x-y plane is they talk about the set having the points (x,y) such that... Well, (x,y) is not on a number line! You know that as well as I do!
 
Jomo said:
No! There are two variables so you are in the x-y plane. Since x>0 and y>0, that puts you in quadrant 1. Now, in quadrant 1, draw the inequality x<y

The key to see that you are in the x-y plane is they talk about the set having the points (x,y) such that... Well, (x,y) is not on a number line! You know that as well as I do!
Click to expand...
1643248226266.png

That makes a lot of sense, thank you!
 
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