# Tagged Questions

44 views

### prenex equivalence problem

Suppose: $$\forall x\exists y \phi(x,y) \to \neg \exists x\psi(x)$$ which of the following formula are prenex normal equivalence with the above formula? i didn't any idea to explain it. it's a ...
79 views

### Combination Problem Understanding

How many ways can a Doctor go to the Hospital on $5$ days of January (which has $31$ days) such that no two visits are on consecutive days? I think the solution is: $\displaystyle\binom{27}{5}$ But ...
39 views

### Partition Graph Challenging Question

I want to find in which of the following Graph, the edges cannot partitioned to triangles? Km,n,r means 3-Partite Complete Graph with m, n, and r sections. a) K7 b) K12 c) K3,3,3 d) K5,5,5 i ...
14 views

### Planner Combination Problem on Graph

I ran into a Graph Problem. Suppose G is A Planner Graph with 100 Vertices such that if connect each two Non-adjacent vertices, the resulting graph would be non-planner. what is the number of edges ...
38 views

### Perfect Matching Combination Problem

We know: A perfect matching (a.k.a. 1-factor) is a matching which matches all vertices of the graph. if we remove edges of perfect matching of a 12-Complete Graph. how many triangle remain in this ...
46 views

### Computable Set & Function

we know that i read this sentence are true? can anyone say an example for following sentence? there are a non computable set A such that
12 views

### Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid?

Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid? For a matroid, the codomain of the weight function is $[0,\infty)$, from Wikipedia ...
43 views