# 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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### proving set theory union statements

I just started learning set theory in discrete mathematics and it's soon enough before i get stuck at my first supplementary question. Prove $( A \cap B) \cup ( A \cap B^c ) = A$ How do i even ...
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### What are “words”?

Related but not duplicate. I am reading Classical Mathematical Logic by Richard L. Epstein, page $3$: B. Types When we reason together, we assume that words will continue to be used in the ...
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### A question in set theory about intersection of two groups.

I've reached the answer, that Cn = to all prime numbers, but i really didnt know how to put it on paper and how to prove its right. I would thank your help.(question below) Question
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### what does “a set of sets that are not members of themselves” of Russell’s Paradox mean

Russell’s Paradox begins with a statement of "Let $R$ be the set of sets that are not members of themselves", i.e. $R=\{S\mid S\notin S\}$. I'm a little bit confused with the statement, for example, ...
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### oblath's result in perfect powers

What do you mean by this statement? Obl\'ath proved that the only perfect powers all of whose digits are equal to a fixed one $a \neq 1$ in decimal representation are 4, 8 and 9. This is equivalent ...
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### How do I find the powerset of $A\cap B$?

$A = \{0,1\}$ $B = \{1,2\}$ My Working : $P(A\cap B)= P(\{\varnothing, \{1\}\}) = \{\varnothing,\{1\},\{\varnothing,\{1\}\}\}$ But the correct answer is $P(A\cap B)= \{\varnothing , \{1\}\}$.
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### Derivative of quadratic form involving singularity

This might be a silly question, but i have been really curious about the following: Consider the following function seen thru a single variable, say $\alpha$: f(\alpha) = \mathbf{x}^...
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### Bound on binomial summation

The bound for $\sum_{i=1}^n\binom{n}{i}2^i$ is $O(3^n)$ but what will be the bound for $\sum_{i=1}^{\frac{n}{2}}\binom{n}{i}2^i$. Any idea how should I proceed.
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### How to remap continued fractions from $\mathbb{R}$ to a discrete set of integers

Assuming that I have a continuous fraction x = a_0 + k_1 \cfrac{x_1}{a_1 + k_2 \cfrac{x_2}{a_2 + k_3 \cfrac{x_3}{a_3 + k_4 \cfrac{x_4}{a_4 \ddots } } } } \end{...
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### Solving a nonlinear equation $\sum_{z=0}^{s} \frac{(\lambda(l-x))^z}{z!} e^{-\lambda(l-x)}=p$

I would appreciate it if someone helps me with solving the following equation. Suppose $\lambda,l \in R^+$, $p\in[0,1]$, and $s\in N_{0}$. How can we find an $x\in [0,l]$, which satisfies the ...
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### How to read partial ordering in a set?

Let $X$ be a partially ordered set with partial order $\preceq$. Then how can we read $x\preceq y$. Is it $x$ less than or equal l to $y$.?
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### Let $R$ be a relation on a set $A$. Show that if $R \circ R \subseteq R$, then $R$ is transitive

On a recent quiz I encountered the problem: Let $R$ be a relation on a set $A$. Show that if $R \circ R \subseteq R$, then $R$ is transitive. I gave the following answer: Assuming $R$ is a relation ...
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