NOTE: Since this is a copy from last years journal, I have yet to add the CSS to make my answers red. You can therefore just assume I picked the correct answers 🙂
So finally it is here, the mysterious course called Discrete Math. Since I first started to interest myself in digital forensics, I have heard about this type of mathematics. I did of course Google it and watched some Youtube-videos on the subject, but if anyone asked me to explain it to them – I really had no answer. Well, as I have learned by now – very few can say what it is, rather say what it isn’t. Brian Hopkins says this on the subject; there is no exact definition of the term “discrete mathematics” (B. Hopkins, 2008). So perhaps the next 6 weeks of studying nothing but discrete math will give me the answer.
First off is something I am kind of fond of, logic theory. First of was an introduction and an activity sheet. This is how I solved it.
Task one we are supposed to fill in the blanks. My answers in red:
1. A universal statement asserts that a certain property is true for all elements.
2. A conditional statement asserts that if one thing is true then some other thing also is true.
3. Given a property that may or may not be true, an existential statement asserts that at least one for which the property is true.
4. A statement is formally called a proposition in Discrete Mathematics.
Second task we had to look at different arguments and rewrite into logical forms.
1. All men are mortal. Socrates is a man. Therefore Socrates is mortal.
The variables here are men (m), mortal (o) and socrates (s):
m are o.
s are m.
Therefore, s are o.
2. If tomorrow is Monday, then it will rain. Tomorrow is Monday. Therefore, it is going to rain.
The variables here are tomorrow (t), Monday (m) and rain (r):
If t are m, then r.
3. All whales are mammals. All mammals are warm-blooded. So all whales are warm-blooded.
The variables here are whales (w), mammals (m) and warm-blooded (b):
w are m.
m are b.
Therefore, w are b.
Makes perfect sense, doesn’t it? Wether or not this is correct remains to be seen later on.
For the third task we had to find the common form of each argument. I am not going to mention all of them here now, but my favorite part was this (my answers in red):
2b. My mind or logic is confusing. My mind is not confused. Therefore, logic is confusing.
Also, one mathematical treat they gave us was this one:
4a. If n is divisible by 6, then n is divisible by 3.
If n is divisible by 3, then the sum of the digits of n is divisible by 3. Therefore, if n is divisible by 6, then the sum of the digits of n is divisible by 3.
This is kind of what I call circus math, its math done funny. Lets say n is actually 18, 42 or 96 – all these three numbers are divisible with 3 and 6. And if you sum the digits of n together you get 9, 6 and 15. Which is all divisible by 3.
Alright, moving on.
The next we had to do is evaluate wether or not this is a statement or not a statement. I have marked all that are statements in red:
1. Snow plus wind means it’s a cold day.
2. Today is Friday.
3. He likes staying in bed until lunchtime.
7. The difference of two primes.
8. Washington D.C. is the capital of New York.
9. How are you?
10. Discrete Mathematics lectures start at 10am.
As you can see, it is easy to spot the difference.
For the rest of the tasks, I did only “browse” them as they are very much similar to these. Only in different form and to distinguish between the three different statements; universal, conditional and existential. And of course, combinations of there.