# Questions tagged [sets]

Questions about finite and infinite sets and multisets, related data structures and concepts.

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### Is every subset of a decidable set, also decidable?

Is it true that if A is a subset of B, and B is decidable, than A is guaranteed to be decidable? I believe it would be true because all the subsets of B should also be decidable making A decidable. I'...
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### Concatenation of the intersection of two languages

I'm enrolled to a Formal Language And Automata course, and we have to prove this equation on sets of strings: $$(L_1\cap L_2)\cdot L_3 ≠ (L_1\cdot L_3) \cap (L_2\cdot L_3)$$ I've tried a lot of sets ...
52 views

### Prove that $|P(X)| = 2^{|X|}$ [closed]

Prove that for any finite set $X$, $|P(X)| = 2^{|X|}$. The solution should use induction.
52 views

### Finding users covering a set x by x

I have a Set $S$ of objects, a set $U$ of users and a map $c: U \rightarrow S^{\prime}$, where $S^{\prime} \subset S$ and $\emptyset \notin S^{\prime}$. Every time I add a new entry to $c$, i.e. ...
123 views

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### Multisets of a given set

A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it counting repetitions. (a) What is the number of ...
259 views

### Finding “fingerprint” sets

Let's say we have 10 people, each with a list of favorite books. For a given person X, I would like to find a special subset of X's books liked only by X, i.e. there is no other person that likes all ...
16k views

### What is complement of Context-free languages?

I need to know what class of CFL is closed under i.e. what set is complement of CFL. I know CFL is not closed under complement, and I know that P is closed under complement. Since CFL $\subsetneq$ P I ...
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### Cantor's diagonal method in simple terms?

Could anyone please explain Cantor's diagonalization principle in simple terms?
147 views

### Functions between sets?

I recently took a practice exam for the Computer Science GRE and this was one of the questions: Assume that set $A$ has 5 elements and set $B$ has 4 elements, how many functions exist from set $A$ ...
242 views

### Computing the rank of a multiset after inserting another element

What is the procedure for computing the rank of a multiset after inserting an element? For instance, lets say we have a set $S = (0,1)$ containing $n = 2$ distinct elements. The multiset $M = (1,1)$ ...
406 views

### Problems for which algorithms based on partition refinement run faster than in loglinear time

Partition refinement is a technique in which you start with a finite set of objects and progressively split the set. Some problems, like DFA minimization, can be solved using partition refinement ...
Given a set $\mathbf{S}$ of sets, I’d like to find a set $M$ such that every set $S$ in $\mathbf{S}$ contains at least one element of $M$. I’d also like $M$ to contain as few elements as possible ...