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Can we have an option to disable notifications on community wiki posts? Prove using natural deduction $((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$ How do I prove the following using Natural Deduction?  $$((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$$   My current approach:  So instead of proving $(P \rightarrow R) \lor (Q\rightarrow R)$, I figure I just need to prove $(P \rightarrow R)$ and use disjunction introduction.  The problem is my hypothesis requires $P$ and $Q$. How do I "create" this Q? I tried using the Law of the Excluded middle, but it does not seem to work.  Any help or insights is deeply appreciated. Footnotes in tables? Where does the word "dog" come from? Disable COPY drag and drop in Windows Explorer in Windows 7 What command(s) would you use to extract all of the usernames from a database called /etc/passwd and then sort this output alphabetically in reverse order? Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$ How to make left-right transition of overlay image ffmpeg I had this "almost bonus" question on the final in Group Theory recently: prove that there is no such group $G$ which would satisfy Aut$(G)\cong \mathbb{Z}_n$, where $n$ is an odd integer. I don't have much certainty if this proof is OK, and one's opinion would be appreciated.  Here's my attempt:     Suppose that there exists such a group $G$ that satisfies the above condition. Since $\mathbb{Z}_n$ is cyclic, Aut$(G)$ is also cyclic and $G$ is abelian, which implies that Inn$(G)\cong \{e\}$. Thus Aut$(G)=$Out$(G)$. (I don't think this fact is important here though). Now, since an automorphism sends a generator to a generator, and since each automorphism is completely determined by such mapping, |Aut($G$)| must be of factorial order. But an integer factorial is always even. However, $|\mathbb{Z}_n|$ is odd, which is a contradiction. Therefore, no such $G$ exists.   I'm afraid that my proof is not very nice, but at least a genuine attempt was made. Calling a parent window function from an iframe I have scripts calling other script files but I need to get the filepath of the file that is currently running within the process.   For example, let's say I have three files. Using :   script_1.py calls script_2.py.  In turn, script_2.py calls script_3.py.    How can I get the file name and path of script_3.py, from code within script_3.py, without having to pass that information as arguments from script_2.py?  (Executing os.getcwd() returns the original starting script's filepath not the current file's.) How can I echo a newline in a batch file? How can you you insert a newline from your batch file output?  I want to do something like:  echo hello\nworld   Which would output:  hello world Mouse sensitivity in 14.04 dissapeared If I go to "Settings -> Mouse &amp; Touchpad" in Ubuntu 14.04 all the options are gone! How can I bring them back? When is a gerund supposed to be preceded by a possessive adjective/determiner? Here's Prob. 3, Chap. 3 in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition:      If $s_1 = \sqrt{2}$, and $$s_{n+1} = \sqrt{2 + \sqrt{s_n}} \ \ (n = 1, 2, 3, \ldots),$$ prove that $\left\{ s_n \right\}$ converges, and that $s_n &lt; 2$ for $n = 1, 2, 3, \ldots$.    My effort:   We can show that $\sqrt{2} \leq s_n \leq 2$ for all $n = 1, 2, 3, \ldots$. [Am I right?]  Then we can also show that $s_n &lt; s_{n+1}$ for all $n = 1, 2, 3, \ldots$. [Am I right?]  But how to calculate the exact value of the limit? Where does this sequence occur in applications? Scripting `rm` and `rm -i` I want to create a script that whenever there are more than three files being removed, it invokes rm -i by default. I know it will go in initialization files but can't seem to get it working.  So far:  if [$file -ge 3]; then   rm -i    exit 0  else   rm exit 1 Blade of the Ruined King Vs. The Bloodthirster Effects:  +25 attack damage +15% life steal +40% attack speed Passive  Unique: Your attacks deal 5% of the target's current health in physical damage (60 max vs minions and monsters). Active   Unique: Drains target champion, dealing 15% of the champion's maximum Health in physical damage and healing you by the same amount. Additionally you steal 30% of their movement speed for 4 seconds - 60 second cooldown. (500 range)  Cost: 3200g VS.   Effects:  +70 attack damage +12% life steal Passive: Gain +1 attack damage and +0.2% life steal per kill (maximum +30 attack damage and +6% life steal). Half of the bonuses are lost upon death.  Cost: 3200g What is better for what situations, and when should you build BT instead of BotRK and Vice Versa. Which provides more lifesteal, the only variable being the stats of the weapon? I find myself constantly questioning my decision on which weapon to get and would really love some in depth answers. Would be great if any examples given were given from the ADC side of the house. An elementary question regarding a multiplicative character over finite fields Reading Chapter 2 of Koblitz's Introduction to Elliptic Curves and Modular Forms, I got stuck on the following question. I would like to proceed my reading, so I would appreciate any hint to this. I have no background in Algebraic Number Theory, but if someone explains in that language, I would like to see it and learn it as much as I can at this moment. References will also be appreciated!  Let $q$ be a power of prime $p$ such that $q \equiv 1 \mod 4$ and $p \nmid 2n$.  Question. Let $\chi_{4} : \mathbb{F}_{q}^{*} \rightarrow S^{1}$ be the character of order $4$, show that $\chi_{4}(-4) = 1$.  The hint in the book says we may show that $\chi_{4}(4) = \chi_{4}(-1) = 1$ for $q \equiv 1 \mod 8$ and $\chi_{4}(4) = \chi_{4}(-1) = -1$ for $q \equiv 5 \mod 8$.  If $q \equiv 1 \mod 8$, then $\chi_{4}(4) = \chi_{4}(2)^{2} = \chi_{2}(2) = \pm 1$, where $\chi_{j}$ denotes the character of order $j$. So I think $2$ must be quadratic residue in this case, but I cannot figure out why. How can I reset my Ability Points? I'm also curious about being able to reset my points, should I wish to change my ability configuration later.  So far (10h-ish) I've only seen one way, which is a potion sold by Kiera Metz for 1000g. However she's no longer available as a store, due to a story choice, so I'm not sure where else I could buy this potion.  Where might I buy this potion, and is it the only way to reset your ability points? What does the draft mode change?