## Assuming a set is decidable, prove that another set is decidable

Suppose we’re dealing with programs that output zeros and ones. Consider all such programs (in a fixed language) having at most n instructions. For each program in this finite set, look at how many ones the program produces when we run it on the empty argument. Call this number one(n).

Consider the set $$\{\langle a,b\rangle :one(a)=b\}$$ where $$\langle \rangle$$ is the Cantor pairing function. Assuming that this set is decidable (there is an oracle telling us the answer), how to prove that $$K=\{x:\phi_x(x)\downarrow\}$$ is decidable? (i.e. how to show that $$K$$ is decidable using that set above as an oracle)

## Can you cast a spell you know from one class as if it was a spell from another? [duplicate]

This question already has an answer here:

• Can I multiclass and cast a spell I already know as a different class? 1 answer

Bards can use a musical instrument as a spellcasting focus for bard spells.

If I have levels in both the Bard and Sorcerer classes, a musical instrument to use as a spellcasting focus, no access to an arcane focus, and a known Sorcerer spell that also appears on the Bard spell list but needs a material component (such as Invisibility), can I cast the Sorcerer spell as if it was a Bard spell? Since it is a Bard spell, I know it, and I have a spellcasting focus for it.

## Is there a way to add a featured image for the product to show in the product listings, but display another image as the product image?

I want to show a different image of products listing on the home page of the site, not the featured image but when customers click on the products then it should show the featured image on the product page. The site is on woocoommerce is there any way to do this. Thanks

## Another Subset sum problem

Verify that (S = {83, 88, 93, 67, 57, 89, 78, 51, 95, 98, 69, 49}, t = 492) is a positive instance of Susbset Sum.

## How to add another parameters to WP_Query?

I need to do something like that:

        $postsOrder = get_sub_field('posts-ordering'); if ($  postsOrder = 'post_views_count') {             $queryPopular = array ( 'meta_key' => 'post_views_count', 'orderby' => 'meta_value_num', ); }$  query = new WP_Query(             array(             'posts_per_page' => $postsCount, 'post_type' =>$  postsType->name,             'order' => 'DESC',             'orderby' => $postsOrder, 'taxonomy' =>$  postsTaxonomy,             $queryPopular ), );  The point is that if$ postsOrder is equal ‘post_views_count’, then in \$ query should be added two another parameters. How to do it right?

## Retrieving the evaluation result of an Initialization Cell in a notebook nb1 from another notebook nb2

I have a very long code in a notebook nb1 in which all the initialization cells are tagged. I have another notebook nb2 where I want to evaluate the initialization cells in nb1 and get the results in nb2 by using CellTags.

I tried the following code, which does something but I cannot see the results in nb2.

myButton[tag_] :=  Button["Evaluate " <> tag,  NotebookEvaluate[ "C:\Users\ttemel\Desktop\World_Bank_projects\WB_Contract_2\\ Extension_to_1st_contract_27oct19\IOdatabase_oecd\database_IOtables_\ SA_NO_UK_2000_2015_run_1.m", EvaluationElements -> {"Tags" -> {tag}}], Method -> "Queued"]; Grid[{Map[myButton, {"SectorIOMarketChains", "DensityPlot"}]}] CellPrint[ ExpressionCell[Defer[Print["SectorIOMarketChains"]], "Input",  CellTags -> {"SectorIOMarketChains"}, ShowCellTags -> True]] CellPrint[ ExpressionCell[Defer[Print["DensityPlot"]], "Input",  CellTags -> {"DensityPlot"}, ShowCellTags -> True]] 

Why does not this code give me the results in nb2?

## Linking Subtype table to another table in EERD

I made this Enhanced Entity relationship diagram for my database project, but there is a problem that I have been mulling over. Over here, it can be seen that MANAGER is under the supertype of EMPLOYEE. I’d like One manager to manage one department. But instead, in the EMPLOYEE supertype table, I have already linked many to one cardinality to the DEPARTMENT table, which means, many employee can work in one department. However, I do not want to mean that many Managers work in one department. How do I fix it?

## Can you use your action to interrupt another player action that was played in the same round?

I think the title is pretty straight forward, I’ll just add some context.

I play in a game when everyone play the way we want at our own turn : saying to another player what he should do is forbidden. Your turn = your action.

I think this is pretty fun and it add a lot of stress in difficult fights since we can’t coordinate ourselve on runtime but, sometime, someone make a mistake that could be avoided in a roleplay way.

So, is it possible to use our own action to interrupt another player action that was played earlier in the same round ?

Thanks.

## What feats or another options can help to avoid touch attack?

If character have only 10 DEX, he becomes vulnerable for touch attacks, because this kind of attacks don’t count the armor. What feat i can take, or what i must do to avoid this attacks, or at least reduce the damage?

I’m interested in avoiding melee touch attacks by keep my AC high against it.

Sources of races, and classes presented in question: Fiendish Codex: Tyrants of Nine Hells Complete Psionic Player’s Handbook

You may use any additional sources to answer.

Hellbred