# 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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### warshall algorithm on excel

How can I implement the warshall algorithm on microsoft excel? What I need: -The user input the matrix R [Relation] -then user gets matrix R infinity matrix How is it possible? It is for an assignment....
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### 100-level discrete maths, induction problem, prove $n^2 \ge 2n + 1$

I've just run into this problem, and was able to go as far, and understand the induction step up to the bolded section. The last part I found in the back of my book, italicized, I can't understand. ...
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### First order logic expression of “Each finite state automaton has an equivalent push-down automaton”?

Problem is Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such ...
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### Switching the order of summations.

Why is the below statement true? $$\sum_{j=0}^{n}\left(-\sum_{t=0}^{k}{{k+1}\choose {t}}j^t(-1)^{k+1-t}\right) = -\sum_{t=0}^{k}{{k+1}\choose {t}}(-1)^{k+1-t}\left(\sum_{j=0}^{n}j^t\right)$$ More ...
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### How many $3$ integer subsets have no consecutive integers, where integers are less than $20$?

I have to determine how many integers between $1$ and $20$ are possible if no two consecutive integers are in a set. I've thought it has something to do with a combination of an element $(a,a+2,a+4)$ ...
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### Say we have a double-decker Lazy Susan with two levels that can be turned independently. If we have n + k dishes in total, how many ways

Say we have a double-decker Lazy Susan with two levels that can be turned independently. If we have n + k dishes in total, how many ways is that solution is correct ???
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### Discrete Math logically equivalent?

Show that $$(p \land q) \lor (\lnot p \land \lnot q) \equiv p\leftrightarrow q$$ How would I go about doing this? Do I use a truth table or a more "algebraic" process?
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### discrete finite summation of non-linear functions

Does anyone have idea for dealing with the two following series summations $$\sum_{i=1}^n \dfrac{1}{a+b x_i}=c$$ $$\sum_{i=1}^n \dfrac{x_i}{a+b x_i}=d$$ I need to find the values of 'a' and 'b'...
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### Let $p \neq \pm 1, 0$ be an integer. Prove that $p$ is prime iff for all $a \in \mathbb Z$, either $p \mid a$ or $(a, p) = 1$.

I'll try in $\to$ direction; Nothing divides the prime $p$ but $\pm1, \pm p$. If $a = \pm p$ or $a = \pm 1$ then $p \mid a$. Assume $p = 2$ . If $a$ is even, then $p \mid a$ and if $a$ is odd, then ...
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### Hanging a painting with nails so that removing any subset of nails from a given collection makes painting fall, and subsets are minimal

So I'm aware of the result that for positive integers $k \leq n$ it's possible to hang a painting with $n$ nails, such that if any $k$ nails are removed then the painting falls, but never when $k-1$ ...
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### Proof - Uniqueness part of unique factorization theorem

The uniqueness part of the unique factorization theorem for integers says that given any integer $n$, if $n=p_1p_2 \ldots p_r=q_1q_2 \ldots q_s$ for some positive integers $r$ and $s$ and prime ...
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### Must the number of people at a party who do not know an odd number of other people be even

I have a homework question in my discrete mathematics class as the title shows, I feel the answer is no, but googling this question seem's to contradict my answer. Let me explain: So if they are ...
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### X and Y be finite sets and f: X->Y be a function.

The option D is the correct option. But, I have a doubt since the inverse of function can exist or cannot exist, how can this option be true. How to approach these questions? Should we assume ...
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### Is p|(q|r) is it equivalent to (q and r)

Using De Morgan's laws can I turn $p|(q|r)$ into: $(q \ and \ r)$ or does the and become an or, such as $(q \ or \ r)$ ?
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### Finding the recurrence relation(with square roots) [closed]

I came across a very peculiar recurrence relation : $\sqrt {T(n)} = \sqrt {T(n-1)} + 2 \sqrt {T(n-2)}$ And Initial Condition $T(0) = T(1)= 1$ Any helps on how to find it
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### How many zero-sum $n$-tuples are there?

The question is extremely short and concise. How many $n$-tuples $X \in \{\, -1,0,1 \,\}^n$ have the zero-sum property $\sum_{x \in X} x = 0$ ? At the moment I have nothing to share of my own since ...
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### Obtain cycles with $a <$ nr. of edges $< b$

I have a chemistry/mathematical problem and I would like to get your opinion. Imagine you are generating a planar, cyclic molecule, with a total $N$ is the number of atoms. By Euler graph theory, the ...
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### Prove by contradiction $a,b,c>0$?

Suppose $a,b,c$ are real numbers such that $a+b+c>0$, $ab+bc+ca>0$, and $abc>0$. Prove by contradiction that $a,b,c>0$. I have tried to solving it case by case like: case $1$: $a,b,c<0$...