### Discrete Mathematics (Statement)

1) x^2 + x + 1 = 0 , x is a real number.Answer: Is a statement. 2) x^2 + x + 1 = 0 , x is complex number. Answer: Is not a statement. Why the question no.2 is not a statment ?...Read more

1) x^2 + x + 1 = 0 , x is a real number.Answer: Is a statement. 2) x^2 + x + 1 = 0 , x is complex number. Answer: Is not a statement. Why the question no.2 is not a statment ?...Read more

I need to create a turing machine that accepts the language a^1 b^j c^k where i >= j >= k, but I am not even really sure how to start. Turing machines in this context are a hard concept for me to grasp for some reason....Read more

I've trying to convert a given BNF list to EBNF and im completely clueless how. Can anyone help?The BNF is: <Sentence> :== <NounPhrase><VerbPhrase><NounPhrase> :== <Noun><NounPhrase> :== <Article><Noun><NounPhrase> :== <Article><AdjectiveList><Noun><NounPhrase> :== <AdjectiveList><Noun><AdjectiveList> :== <Adjective><AdjectiveList> :== <Adjective><AdjectiveList><VerbPhrase> :== <Verb><VerbPhrase> :== <Ver...Read more

Come up with a proposition p(n), depending on n, such that p(1), p(2),...,p(999) are true, but p(1000) is false.I don't really understand the question but my proposition is that p(n) < p(1000)1 < 1000 is true and when it is 1000 < 1000 it is false. Do I have to come up with an equation for p(n)?...Read more

So the question is A0 = 4, A(n)=A(n-1) - n So far what I have is A(1)=3, A(2)=1, A(3)=-2, A(4)=-6.I understand how to get those numbers and I could infinitely go up if I wanted to. But I'm having a hard time understanding the logic to finding the solution.Thanks guys!...Read more

I've to describe a recurrence for l_n, the number of lobsters caught in year nThe task says: A hobby fisherman estimates the number of lobsters he will catch in a year as the average of the number he caught in the two previous yearsDescribe a recurrence for l_n, the number of lobsters caught in year nI've tried something. It's degree-D homogeneous LRR so the recurrence is:l_n = l_n-1 + l_n-2 as it's for 2 years. Have I solved ít correctly?...Read more

So I need to find a_30 for a recurrence relation defined by: a_n=2*a_n/2 + 1a_1=1Underscores dictate subscripts.The dilemma I run into: in order to find a_30, I must find a_15, but to find that I need a_7.5, which simply doesn't exist. How do I handle this? I also tried running it in Matlab, but it predictably terminated on a_3, citing the same type of nonexistent index....Read more

I'm new to recurrence relations and I'm having trouble figuring out this problem:Find a recurrence relation for the number of ways to make a stack of green, yellow, and orange napkins so that no two green napkins are next to each other.I've come up with a(n)=2a(n-1)+2a(n-2) but I'm not sure if that's right/ on the right track.Any help would be great!...Read more

I am having problems proving this set equivalence (discrete mathematics) B∩~(~B∩~B)=BI've used double negation, de morgans and then the associative law but I can't quite get there....Read more

I am looking for a method to compute a derivative using a discrete and fast method. Since now I do not know the type of equation I have, I am looking for discrete methods analog to the ones that we can find for the integral such as, the Euler method....Read more

Discrete mathematics (also finite mathematics) deals with topics such as logic, set theory, information theory, partially ordered sets, proofs, relations, and a number of other topics.For other branches of mathematics, there are tools that support programming. For statistics, there is R and S that have many useful statistics functions built in. For numerical analysis, Octave can be used as a language or integrated into C++. I don't know of any languages or packages that deal specifically with discrete mathematics (although just about every lang...Read more

Inspired after watching Michael Feather's SCNA talk "Self-Education and the Craftsman", I am interested to hear about practical examples in software development where discrete mathematics have proved helpful....Read more

I'm taking a discrete mathematics course, and I encountered a question and I need your help. I don't know if this is the right place for that though :)It says:Each user on a computer system has a password, which is six to eight characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there?The book solves this by adding the probabilities of having six,seven and eight characters long password. However, when he solves for probability of six characters h...Read more

Is this statement true ? ∀x ∈ R, ∃y ∈ R,(x ≥ y) ⇒ (x > y)I believe it is not because for example if x is 5 and y is 5 it satisfies "(x ≥ y)" but it doesn't mean that it is also "(x > y)". Am I correct ? Your input would be much appreciated....Read more

I would like to be sure that my answer is true.the question is :Let I (x) be the statement “x has an Internet connection”and C(x, y) be the statement “x and y have chatted overthe Internet,” where the domain for the variables x and yconsists of all students in your class. Use quantiﬁers toexpress each of these statements:** Exactly one student in your class has an Internet connection.my answer is: ∃x∀y(x=y ↔ I(y))....Read more