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!!