# Tagged Questions

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

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### How do you find the order of a recurrence relation?

I cannot find a straight forward answer in my book or online. A lot of the answers I found are very wordy and I have trouble understanding them. For example take this recurrence relation: Is the ...
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### Clarification on a reflexive function

$R_1 = \{(a, b) | a โค b\}$ is a reflexive function, but I'm confused on why it is. $aโคb$ but doesn't that not necessarily mean that there is an $a$ that will equal $b$? Couldn't all of the $a$ very ...
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### Confusion on sets and relations

I'm confused on how the number of subsets equals the number of relations. If set A = {1, 2} then AxA would be {}, {1}, {2}, {1,2}. I'm confused on how there are $2^{n^2}$ subsets of $A$ x $A$ because ...
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### A question related to linear recurrence.

I have seen examples such as Towers of Hanoi and Merge Sort, which I understand but when it comes to solving this kind of problems I just don't understand where to start. If given a solution to the ...
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### Discrete Mathematics Nonhomogenous linear recurrence relation

Solve the recurrence relation $$a_n=-a_{n-1}+8a_{n-1}+12a_{n-3}+25\cdot3^{n-2}-18n^2+48n+14\text{ for }n\ge3$$ where $a_0=6,a_1=0$ and $a_2=57$. Just want to ask if my $p_n$ is correct because I ...
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### Given that the relation that aRb if and only if the smallest element of a is is equal to the smallest element in b?

X is the set of all nonempty subsets of the set {1,2,3,4,5,6,7,8,9,10}. a,b are elements of X. a) Find the number of elements in the equivalence class [{2,6,7}]? ...
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### Worst Case Time Complexity Analysis of an Algorithm

Below I have an algorithm for finding the mode of a list of nondecreasing integers. I'm trying to analyze the time complexity of this algorithm. Procedure find a mode($a_1, a_2, ..., a_n$:...
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### If Mr. X was born on April 16, 1987 what day is 2016 days after he was born?

I have a confusion about the way of solving the following mathematical problem: If Mr. X was born on April 16, 1987 what day is 2016 days after he was born? How will I solve these kind of ...
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### Choose a point which minimizes the sum of distances between it and other points in set explanation

I was wondering, suppose I have a set of integers, {1, 70, 97, 98, 99, 101, 102}, what is the integer to choose such that the distance is minimised for a subset ...
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### $10$ people are standing in a queue when three new checkouts open. In how many ways can the three new queues be formed?
Problem: $10$ people are standing in a queue when three new checkouts open. 8 people rush to the new checkouts and the new queues end up with at least two people in each. In how many ways can the ...