Sets and set operations??

[bubbagump]

Hello~
I'm not sure if this is exactly where it goes...but we'll see.

List the elements of the set in roster notation. (Enter Ø for the empty set.)
{x | x is a letter in the word HIPPOPOTAMUS}

We're doing sets and set operations...and I have not the slightest idea of what to do. The first question I guess would be what elements?? Thank you!!

 

[soroban]

Hello, bubbagump!

List the elements of the set in roster notation. (Enter Ø for the empty set.)

. . {x | x is a letter in the word HIPPOPOTAMUS}

Either someone explained this badly or someone isn't comprehending the concepts.

$\displaystyle \text{When we are given: }\;\{\,x\,|\,f(x)\,\}$

. . $\displaystyle \text{The braces }\{\} \text{ mean: "The set"}$
. . $\displaystyle \text{the first }x\text{ means: "all }x"$

. . $\displaystyle \text{the vertical line means "such that"}$

. . $\displaystyle f(x)\text{ is the condition that must be satisfied.}$


$\displaystyle \text{So our problem says: "The set of all }x\text{ such that }x\text{ is a letter in HIPPOPATOMUS".}$

$\displaystyle \text{The letters in that word are: }\:H,\,I,\,P,\,O,\,A,\,T,\,M,\,U,\,S$
. . (Do not include duplicates.)

$\displaystyle \text{So the answer is: }\;\{H,\,I,\,P,\,O,\,A,\,T,\,M,\,U,\,S\}$


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Another example:

$\displaystyle \{x\,|\,x\text{ is a month whose English name begins with J}\,\}$

. . . $\displaystyle =\;\{\text{January},\,\text{June},\,\text{July}\}$

 

[bubbagump]

Oh okay! Thank you. Yes, we had a substitute teacher and that's probably why...he didn't explain it very well!!