Discrete Mathematics Problem dealing with sets

[Faxon]

Hi, I'm a student of the University of Missouri--columbia and I'm having a very difficult time with this course. I can hardly understand my instructor and the examples in the book don't help. I've been working on this problem:

Let, A = {n is an element in Natural numbers: N<= 20}, Determine the following sets:

(c) {n is an element of A: max{n,4} = 4}
(d) {n is an element of A: max{n,14} = n}

I think c is just {1, 2, 3, 4} but I have no idea what (d) is. If you could explain to me the full process of how to do this, that would be awesome.

 

[pka]

Try \(\displaystyle \{14,15,...,20\}\).

 

[Faxon]

I need help in breaking down part (d). I don't see why it would 14, 15, 16...20? I thought max was that was as high as it would go? And isn't it {n,14} a pair? Like {1, 14}, {2,14}...{20,14}? But, I'm confused of why it's equal to n at max.

 

[daon]

The mathematical statement "max{n, 14}=n" literally translates to "The maximum of a number and 14 is that same number." A more friendly version might read, "The numbers that when compared to 14, are bigger or equal."

Those members of A for which the above statement holds true would be the members of the set in (d). The statement would not be true if n < 14, but true if 14 <= n <= 20.

 

[Faxon]

Thanks a lot, so what about (c)? I'm unclear of the "=n and =4" parts of the sets. If someone could explain that part that would be great. Like I said, no examples in my book nor in my notes over this. So, I have really no clue.

 

[mmm4444bot]

Thanks a lot, so what about (c)? I'm unclear of the "=n and =4" parts of the sets. If someone could explain that part that would be great. Like I said, no examples in my book nor in my notes over this. So, I have really no clue.

I agree with you; you have really no clue. :wink:

The previous post provides the explanation of the notation for you. You indicate that you understand the notation by virtue of your acknowledgment that you have completed part d, yet you still cannot answer part c.

Answer each of the following questions about the elements of set A. When the answer is YES, it indicates that the corresponding element of A is also an element of the set in part c.

Is the greater of 1 and 4 equal to 4?
Is the greater of 2 and 4 equal to 4?
Is the greater of 3 and 4 equal to 4?
Is the greater of 4 and 4 equal to 4?
Is the greater of 5 and 4 equal to 4?
Is the greater of 6 and 4 equal to 4?
Is the greater of 7 and 4 equal to 4?
Is the greater of 8 and 4 equal to 4?
Is the greater of 9 and 4 equal to 4?
Is the greater of 10 and 4 equal to 4?
Is the greater of 11 and 4 equal to 4?
Is the greater of 12 and 4 equal to 4?
Is the greater of 13 and 4 equal to 4?
Is the greater of 14 and 4 equal to 4?
Is the greater of 15 and 4 equal to 4?
Is the greater of 16 and 4 equal to 4?
Is the greater of 17 and 4 equal to 4?
Is the greater of 18 and 4 equal to 4?
Is the greater of 19 and 4 equal to 4?
Is the greater of 20 and 4 equal to 4?

Cheers,

~ Mark

 

[Faxon]

Thanks, Mark! I think I've got it now.

Is the greater of 1 and 4 equal to 4? yes
Is the greater of 2 and 4 equal to 4? yes
Is the greater of 3 and 4 equal to 4? yes
Is the greater of 4 and 4 equal to 4? yes
Is the greater of 5 and 4 equal to 4? no
Is the greater of 6 and 4 equal to 4? no
Is the greater of 7 and 4 equal to 4? no
Is the greater of 8 and 4 equal to 4? no
Is the greater of 9 and 4 equal to 4? no
Is the greater of 10 and 4 equal to 4? no
Is the greater of 11 and 4 equal to 4? no
Is the greater of 12 and 4 equal to 4? no
Is the greater of 13 and 4 equal to 4? no
Is the greater of 14 and 4 equal to 4? no
Is the greater of 15 and 4 equal to 4? no
Is the greater of 16 and 4 equal to 4? no
Is the greater of 17 and 4 equal to 4? no
Is the greater of 18 and 4 equal to 4? no
Is the greater of 19 and 4 equal to 4? no
Is the greater of 20 and 4 equal to 4? no