Completely lost on Sets and Relations

[schoolthrowaway]

I've been spending every hour of 3 days now minus sleep trying to figure out sets & relations for a huge CS concepts exam tomorrow afternoon, and I can't even decipher the questions or notes, and the provided solutions for certain examples make no sense.


i.e. a previous question from a slide example:


---------------


:We​ ​will​ ​use​ ​the​ ​following​ ​sets​ ​in​ ​the​ ​problems​ ​below
S​ ​=​ ​{1,​ ​2,​ ​3,​ ​4}
T​ ​=​ ​{1,​ ​2,​ ​3}
V​ ​=​ ​{2,​ ​4,​ ​6}
W​ ​=​ ​{3,​ ​4,​ ​5,​ ​6}
1)​ ​Define​ ​the​ ​union​ ​operation.​ ​What​ ​is​ ​the​ ​union​ ​of​ ​sets​ ​S​ ​and​ ​V?


Instructor solution:


**Given two sets S and T, the union S ∪ T gives us the set V which contains all elements that x |
x ∈ S or x ∈ T
{1,2,3,4,6} **


--------
how is T remotely relevant to this problem, and how does the union of S and T (numbers that only contain 1,2,3, and 4 for only s) give us V( a set that contains 6)???


and an example problem on the HW:


___________________


Use Venn diagrams to show the following algebraic laws. For each subexpression involved in the equivalence, indicate the set of regions it represents.
a) (S ∪ (T ∩ R)) ≡ ((S ∪ T ) ∩ (S ∪ R))


i havent heard much about any algebraic laws for these, and looking at the slides has no definition for a subexpression or what it refers to in the example, or what 2 things 'equivalence' connects, or what a region is supposed to be.


__________


I'm utterly confused, and haven't found any reliable beginner's guide that refer to specifically this kind of stuff, and all potential tutors have been turning me down for about a week.

 

[tkhunny]

What do you have against T? It's a set. It has elements. Just because all of its elements also appear in S does not diminish the importance of T. Perhaps think of two circles, one entirely inside the other. Is the smaller circle irrelevant simply because it is contained in the larger? One might apply this idea to cities and states. What you are saying about T is that no one can be from Pittsburgh, because we already know they are from Pennsylvania. Be nice to T. We'll need subsets in the future.

 

[stapel]

...the provided solutions for certain examples make no sense. For example, a previous question from a slide example:

---

We​ ​will​ ​use​ ​the​ ​following​ ​sets​ ​in​ ​the​ ​problems​ ​below:

. . .S​ ​=​ ​{1,​ ​2,​ ​3,​ ​4}
. . .T​ ​=​ ​{1,​ ​2,​ ​3}
. . .V​ ​=​ ​{2,​ ​4,​ ​6}
. . .W​ ​=​ ​{3,​ ​4,​ ​5,​ ​6}

1)​ ​Define​ ​the​ ​union​ ​operation.​ ​What​ ​is​ ​the​ ​union​ ​of​ ​sets​ ​S​ ​and​ ​V?

---

Instructor solution:

**Given two sets S and T, the union S ∪ T gives us the set V which contains all elements that x, such that x ∈ S or x ∈ T
{1,2,3,4,6} **

---

how is T remotely relevant to this problem...?

Since the exercise asked for the union of S and V, I have no idea.

...and how does the union of S and T (numbers that only contain 1,2,3, and 4 for only s) give us V( a set that contains 6)?

It doesn't. I have no idea what your instructor has been smoking. :shock:

and an example problem on the HW:

---

Use Venn diagrams to show the following algebraic laws. For each subexpression involved in the equivalence, indicate the set of regions it represents.

. . .a) (S ∪ (T ∩ R)) ≡ ((S ∪ T ) ∩ (S ∪ R))

---

i havent heard much about any algebraic laws for these, and looking at the slides has no definition for a subexpression or what it refers to in the example, or what 2 things 'equivalence' connects, or what a region is supposed to be.

The laws were supposed to have been covered in class, and listed and explained in your textbook. Likely, they're something along the lines of what is contained in this PDF.

My guess is that, by "subexpression", the author means "portion of the expressions on either side of the equivalence symbol". So "T ∩ R", "S ∪ T", and "S ∪ R" would be "subexpressions. I think....

Venn diagrams were also supposed to have been taught before homework was assigned on them. To learn what they are, and how their "regions" work, try here.