# BasilMarket

## Chat Forum Talk about topics not related to MapleStory

I'm really bored. Give me math/physics/CS problems. (Math: Anything through Multivariable. Physics: Preferably only before calculus-based E&M).
Or... post whatever you want to talk about/

I have determined that I am too mathematically weak. Will be making a similar thread in 6 months after improving.

# Replies

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Do you know how to program in VB?
Jan 19 2013
Level 104 Scania Aran 3
Happy Birthday
1. If f(0) = 1, f(1) = 3, and f(n) = 2*f(n-1) + f(n-2) for n = 2, 3, 4, ..., what is f(4)?

2. Prove each by formal induction, not some other proof technique:
a. 1 + 3 + 5 + ... + 2n - 1 = n2, for n = 1, 2, 3 ....
b. There are 2n subsets of a set of n elements, for n = 0, 1, 2, ....

3. Express the sum in a closed-form expression: 1 + 3 + 32 + 33 + ... + 3n

4. Consider the statement S: If it is raining, then I carry an umbrella.
a. State the converse of S.
b. State the contrapositive of S.
c. Which of these answers are equivalent to S? (a, b, both, or neither?)

5. Let A B, and C be Boolean expressions, and assume '==>' means 'implies'. Consider the statement S:
[(A or B) ==> C] ==> (B ==> C)
a. Prove S with a truth table.
b. Prove S with a logical argument, giving a reason for each step (assuming a hypothesis and deriving the conclusion)

6. How many subsets with 3 elements can be formed from a set of 12 elements? (You should NOT need to list them all!)

7. Suppose a pair of distinct elements are chosen at random from the set (2, 3, 5, 6). What is the probability that both numbers share a common factor > 1? (Here some listing and counting helps!)

8. Suppose b is a positive number. If by = x, what is y in terms of b and x?

9. Is R = {(1,1), (2,2), (4,4), (1,4), (4, 1)} an equivalence relation on the set S = {1, 2, 4}? If not, what rule is broken? If so, how is S partitioned by R?

10. What is an identity relating loga b, loga c, and logb c?
Jan 19 2013
@GrammarJew:
Nope. Java,Python,C,JScript. Although if you give me time, I should be able to transcribe code from one language to another within 10 minutes if 0 lines. I prefer class-structured languages, so Java is my forte.
Jan 19 2013
Do you know how to program in VB?[/quote]

If Str\$(Input(Answer)) = Yes or Maybe then
OutPut(Question) = "Congrats dawg!"
Else
Quit
End if
Jan 19 2013
@GrammarJew:
Nope. Java,Python,C,JScript. Although if you give me time, I should be able to transcribe code from one language to another within 10 minutes if 0 lines. I prefer class-structured languages, so Java is my forte.[/quote]

I understand. VB is the worst programming language ever. My teacher insists on using it for a project though.
Jan 19 2013
I understand. VB is the worst programming language ever. My teacher insists on using it for a project though.[/quote]

I was forced to only use VB through 3 years of computer science in high school.

Completely forgot how to code efficiently now, so it was useless either way.
Jan 19 2013
Happy Birthday
1. If f(0) = 1, f(1) = 3, and f(n) = 2*f(n-1) + f(n-2) for n = 2, 3, 4, ..., what is f(4)?

2. Prove each by formal induction, not some other proof technique:
a. 1 + 3 + 5 + ... + 2n - 1 = n2, for n = 1, 2, 3 ....
b. There are 2n subsets of a set of n elements, for n = 0, 1, 2, ....

3. Express the sum in a closed-form expression: 1 + 3 + 32 + 33 + ... + 3n

4. Consider the statement S: If it is raining, then I carry an umbrella.
a. State the converse of S.
b. State the contrapositive of S.
c. Which of these answers are equivalent to S? (a, b, both, or neither?)

5. Let A B, and C be Boolean expressions, and assume '==>' means 'implies'. Consider the statement S:
[(A or B) ==> C] ==> (B ==> C)
a. Prove S with a truth table.
b. Prove S with a logical argument, giving a reason for each step (assuming a hypothesis and deriving the conclusion)

6. How many subsets with 3 elements can be formed from a set of 12 elements? (You should NOT need to list them all!)

7. Suppose a pair of distinct elements are chosen at random from the set (2, 3, 5, 6). What is the probability that both numbers share a common factor > 1? (Here some listing and counting helps!)

8. Suppose b is a positive number. If by = x, what is y in terms of b and x?

9. Is R = {(1,1), (2,2), (4,4), (1,4), (4, 1)} an equivalence relation on the set S = {1, 2, 4}? If not, what rule is broken? If so, how is S partitioned by R?

10. What is an identity relating loga b, loga c, and logb c?[/quote]

Ignore this post for now.
Jan 19 2013
Level 104 Scania Aran 3
I understand. VB is the worst programming language ever. My teacher insists on using it for a project though.[/quote]

what class are you using vb for lool?
Jan 19 2013
Level 200 Windia Mercedes 4
template<typename T>
constexpr auto add(T a, T b) -> decltype(a+b) { return a+b; }
Jan 19 2013
@makidua: It's not letting me post all my solutions for some reason. I'll add a bit at a time to this comment.

1.
f(0) = 1
f(1) = 3
f(n) = 2*f(n-1) = f(n -2) for 2,3,4...
f(2) = 2 *f(1) + f(0) = 7
f(3) = 2*7 + 3 = 17
f(4) = 2*17 + 7 = 41

2a. (I proved this for you already)
2b. Do you mean 2^n? 2n is too few. Each element can be either in the subset or outside of the subset, so the answer is simply 2^n because each element only has two possible locations.

3. Guessing it's 1 + 3 + 3^2 + 3^3 + ... + 3^n
This is the sum of geometric sequence. 3(1 - 3^n)/(1 - 3) = 3(1 - 3^n)/(-2)

4

Logic statements:
statement: p --> q
converse: q --> p
inverse: ~p --> ~q
contrapositive: ~q --> ~p

a.If I carry an umbrella, then it is raining.
b.If I don't carry an umbrella, then it's not raining.

Edit:

5a.
A|B|C|D|[(A or B) --> C] --> (B --> C)
T|T|T|T
T|T|F|T
T|F|T|T
F|T|T|T
T|F|F|T
F|T|F|T
F|F|T|T
F|F|F|T
5b. Actually not sure how to do this because I'm rusty with logic (ahah...) But, since everything in the table is true, it can only be true

6.Order does not matter, so it's just 12C3

7. Order matters here. You have 12 total possibilities. 2,3,5 are prime, so your only options are to select a 6 with a 2 or 6 with a 3. Therefore, your chance is 1/3.