## What does it mean to “show algebraically” in propositional logic?

The biconditional operator $$\iff$$ of Propositional Logic can be defined by the identity

$$p \iff q \equiv (\lnot p \lor q) \land (\lnot q \lor p) \quad (1.1)$$

Use the identity $$(1.1)$$ and identities from the list on page 2, to show algebraically that

$$p \iff q \equiv (\lnot p \land \lnot q) \lor (q \land p)$$

State which identity you are using at each step.

What does this question mean by asking to "show algebraically"? I have tried referring to my notes and online search but no luck with a definition! These propositions are already algebraic, are they not? Having some issues understanding the wording of the question. This is from a mock university test. I’m assuming it wants me to demonstrate using a truth table?

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## Buffer overflow Mona modules all show Rebase SafeSEH ASLR True

Almost every beginners (noob friendly) tutorial written for Stack based buffer overflow explains when using mona module to locate a safe reliable memory address for our EIP to JMP to our shellcode should have Rebase, Safe SEH, ASLR disabled. However in a recent stack based buffer overflow challenge, all the modules mona provided showed they were protected except for the executable itself.

I used a module (DLL) that had those protections shown by mona to JMP to my shellcode and successfully execute my shellcode which really confused me.

If the executable itself is not protected does that mean we can use any DLL to JMP to our shellcode? if not what is the proper way to handle this situation?

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## Show that if $\mathcal{H}$ is PAC learnable in the standard one-oracle model, then $\mathcal{H}$ is PAC learnable in the two-oracle model

This is a question $$9.1$$ from Understanding Machine Learning Chapter 3. It goes like this:

Consider a variant of the PAC model in which there are two example oracles: one that generates positive examples and one that generates negative examples, both according to the underlying distribution $$\mathcal{D}$$ on $$\mathcal{X}$$. Formally, given a target function $$f : \mathcal{X} \to {0,1}$$, let $$\mathcal{D}^+$$ be the distribution over $$\mathcal{X}^+ = \{x \in \mathcal{X}: f(x) = 1\}$$ defined by $$\mathcal{D}^+(A) = \frac{\mathcal{D}(A)}{\mathcal{D}(X^+)}$$, for every $$A \subset \mathcal{X}$$. Similary $$\mathcal{D}^-$$ is the distribution over $$\mathcal{X}^{-}$$ induced by $$\mathcal{D}$$.

The definition of PAC learnability in the two-oracle model is the same as the standard definition of PAC learnability except that here the learner has access to $$m^{+}_{\mathcal{H}}(\epsilon, \delta)$$ i.i.d. examples from $$\mathcal{D}^+$$ and $$m^{-}_{\mathcal{H}}(\epsilon, \delta)$$ i.i.d. examples from $$\mathcal{D}^{-}$$. The learner’s goal is to output $$h$$ s.t. with probability at least $$1-\delta$$ (over the choice of the two training sets, and possibly over the nondeterministic decisions made by the learning algorithm), both $$L_{(\mathcal{D}^+,f)}(h) \leq \epsilon$$ and $$L_{(\mathcal{D}^−,f)}(h) \leq \epsilon$$

I am trying to prove that if $$\mathcal{H}$$ is PAC learnable in the standard one-oracle model, then $$\mathcal{H}$$ is PAC learnable in the two-oracle model. My attempt so far:

Note that $$L_{(D,f)}(h) = \mathcal{D}(\mathcal{X}^+)L_{(\mathcal{D}^+,f)}(h) + \mathcal{D}(\mathcal{X^{-}})L_{(\mathcal{D}^-,f)}(h).$$ Let $$d = min \{ \mathcal{D^+}, \mathcal{D^-}\}$$, then if $$m\geq m_\mathcal{H}(\epsilon d, \delta)$$, then it is clear that: $$\mathbb{P}[L_{(D,f)}(h)\leq \epsilon d] \geq 1-\delta \implies \mathbb{P}[L_{(D^+,f)}(h)\leq \epsilon] \geq 1-\delta$$ And, $$\mathbb{P}[L_{(D,f)}(h)\leq \epsilon d] \geq 1-\delta \implies \mathbb{P}[L_{(D^-,f)}(h)\leq \epsilon] \geq 1-\delta$$

So we know that if we have $$m\geq m_{\mathcal{H}}(\epsilon d, \delta)$$ samples drawn iid from $$\mathcal{D}$$, then we can guarantee $$\mathbb{P}[L_{(D^+,f)}(h)\leq \epsilon] \geq 1-\delta$$ and $$\mathbb{P}[L_{(D^-,f)}(h)\leq \epsilon] \geq 1-\delta$$.

How do I choose $$m_{\mathcal{H}}^+(\epsilon, \delta)$$ and $$m_{\mathcal{H}}^-(\epsilon, \delta)$$ such that if we have $$m^+ \geq m_{\mathcal{H}}^-(\epsilon, \delta)$$ samples iid according to $$\mathcal{D}^+$$ and $$m^- \geq m_{\mathcal{H}}^-(\epsilon, \delta)$$ drawn iid according to $$\mathcal{D}^{-}$$, then we can guarantee $$\mathbb{P}[L_{(D^+,f)}(h)\leq \epsilon] \geq 1-\delta$$ and $$\mathbb{P}[L_{(D^-,f)}(h)\leq \epsilon] \geq 1-\delta$$?

When is drawing $$m^+$$ samples according to $$\mathcal{D}^+$$ and $$m^{-}$$ samples according to $$\mathcal{D}^-$$ the same as drawing $$(m^+ + m^-)$$ samples according to $$\mathcal{D}$$?

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## Show postcondition i:=i+1 using Hoare assginment rule

as far as I understand the hoare assignment rule works like:

{i+1=3}i:=i+1{i=3} 

E.g. to get the precondition I take the postcondition {i=3} and replace every occurence of i against i+1.

But what if i want to show that if i holds a certain value before

{???}i:=i+1{i=i+1} 

that after the assignment i is increased by one, i.e. {i=i+1} is true? I cant replace i against i+1, otherwise i will get something like which is

{i+1=i+1+1}i:=i+1{i=i+1}  {i+1=i+2}i:=i+1{i=i+1}       i+1=i+2 is not equal 

Another example:

I want

{i=0}i:=i+1{i=1} 

But replacing i against i+1 in the postcondition I get

{i+1=0}i:=i+1{i=1} 

Something like

{i=i}...i:=i+1{i=i+1}      

would be good

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## Show subcategories broken when WP/WC updates

I’ve been given to mantain a site who wasn’t updated for a while: it had WP 4.9.15 and WooCommerce 2.6.14

Now I’ve made a site test where i’ve updated all these things and now i have WP 5.4.2 and WC 4.3.1

One thing that is broken and i’m not able to figure why is the page showing the products by category: they have a 3 level category tree. It worked this way: if the category asked was a leaf, the page showed the product list. If it wasn’t a leaf, it showed all the subcategories.

The template page doing this is archive-product.php which has this simple loop to show everything:

            <h1 class="page-title"><?php woocommerce_page_title(); ?></h1>              <?php if ( have_posts() ) : ?>                  <?php                     /**                      * woocommerce_before_shop_loop hook                      *                      * @hooked woocommerce_result_count - 20                      * @hooked woocommerce_catalog_ordering - 30                      */                     do_action( 'woocommerce_before_shop_loop' );                 ?>                  <?php woocommerce_product_loop_start(); ?>                      <?php woocommerce_product_subcategories(); ?>                      <?php while ( have_posts() ) : the_post(); ?>                          <?php wc_get_template_part( 'content', 'product' ); ?>                      <?php endwhile; // end of the loop. ?>                  <?php woocommerce_product_loop_end(); ?>                  <?php                     /**                      * woocommerce_after_shop_loop hook                      *                      * @hooked woocommerce_pagination - 10                      */                     do_action( 'woocommerce_after_shop_loop' );                 ?>              <?php elseif ( ! woocommerce_product_subcategories( array( 'before' => woocommerce_product_loop_start( false ), 'after' => woocommerce_product_loop_end( false ) ) ) ) : ?>                  <?php wc_get_template( 'loop/no-products-found.php' ); ?>              <?php endif; ?> 

Now this page works only if the category requested is a leaf thus it has to display a list of products. If the category requested is not a leaf, no subcategory is shown and the page is blank with only the category name (page_title) showing. So it means that the query is somewhat did good, but why no category is shown? Thank you if you can help me solving this trouble

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## filter default wp_query to show just selected level of child pages in wordpress

I’m working on a site that has a fairly large page structure a few levels deep – in some sections there are a lot of pages.

So I want to have functionality if user choose on select box level 1 then only pages in level 1 will show in below list of pages. if he choose level 2 then only level 2 pages, same go to level 3 level 4 level 5 level 6.

it’s working for top level parent pages when I set query_vars[‘post_parent’] = 0; and I want to have same functionality to show list of level 1 child page,level 2 child pages and so on…

I am stuck on it. please I will be great full if anyone can help me for it. Thanks see screenshot link https://i.stack.imgur.com/EKpy6.png

## How to show only homepage in google results instead of privacy, contact pages

When I search my website in google, all the pages and posts can see. I want to make only homepage visible in search results and remove other pages(privacy, contact etc). And also all the posts can visible without snippet. I want to fix this. Please help me. enter image description here

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## Nmap doesn’t show physical hosts

~# nmap -sn 10.0.2.0/24 Starting Nmap 7.80 ( https://nmap.org ) at 2020-07-02 18:11 +01 Nmap scan report for 10.0.2.2 Host is up (0.00068s latency). MAC Address: 52:54:00:12:35:02 (QEMU virtual NIC) Nmap scan report for 10.0.2.3 Host is up (0.00067s latency). MAC Address: 52:54:00:12:35:03 (QEMU virtual NIC) Nmap scan report for 10.0.2.4 Host is up (0.00070s latency). MAC Address: 52:54:00:12:35:04 (QEMU virtual NIC) Nmap scan report for 10.0.2.15 Host is up. Nmap done: 256 IP addresses (4 hosts up) scanned in 2.04 seconds 

i use a virtual machine, and Nmap shows only the virtual hosts