Disprove the statement $f(A \cap B) = f(A) \cap f(B)$ If someone could walk me through this I would greatly appreciate it.  Disprove the following statement:   If $f : X \rightarrow Y$ is a function and $A$, $B$ are subsets of $X$ then $f(A \cap B) = f(A) \cap f(B)$.
Do we have always $f(A \cap B) = f(A) \cap f(B)$? Suppose $A$ and $B$ are subsets of a topological space and $f$ is any function from $X$ to another topological space $Y$. Do we have always $f(A \cap B) = f(A) \cap f(B)$?  Thanks in advance
Why is a home fiber connection asymmetric? I recently switched from an ADSL to a fiber connection and was surprised to see that the bandwidth is asymmetric (1 Gbps down / 250 Mbps up).  While this is understandable in ADSL, I do not understand why fiber at home is asymmetric as well? It is not a limitation of the technology (I have symmetric fiber at the office, and always had) What is the metal sheath surrounding a USB connector, and is it commonly connected? I've been using Windows 10 for a couple of month now (joined the Insider Preview).  Now my hard drive started ticking so I've bought a new SSD and I want to move the windows installation to the new hard drive, which has been connected to the computer (unpartitioned). I don't mind and I even prefer reinstalling it over again.   Since I have the free version of Windows 10 pro, can I still reinstall it anew? Does the windows 10 installation offer disk management and partition like the older Windows installations used to? How should I reinstall Winodws 10 x64 the easiest but still remain on free mode? 3-regular graphs with no bridges Problem. Use Tutte's 1-factor theorem to prove that every 3-regular graph with no bridges has a 1-factor.  I honestly have no idea how to approach this problem. I have drawn a couple of graphs to gain some insight to no avail. Any hints or tips will be greatly appreciated. How to prove this sequent using natural deduction? How do I prove $$S\rightarrow \exists xP(x) \vdash \exists x(S\rightarrow P(x))$$ using natural deduction? Just an alignment of which axioms or rules that one could use would be much appreciated. If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined From Ireland,Rosen's Number Theory book, ex.8.12.  Let $p\equiv1\mod{4}$, then we can write $p=a^{2}+b^{2}$, where $a,b\in\mathbb{Z}$. Now, let $a$ be odd and $b$ be even and $a,b&gt;0$. How can we show that $a$ and $b$ are uniquely determined? The hint says to use the fact that $\mathbb{Z[i]}$ is a UFD and $p=a^{2}+b^{2}\implies a+bi$ is prime in $\mathbb{Z[i]}$ How to measure supply currents ranging from 1μA to 10mA? I want to boot Ubuntu into recovery mode but there is no grub menu entry allowing me to do so. I pressed e and now I am able to edit boot options. It looks like that:  setparams 'Ubuntu , with Linux 3.6.0-26-generic'  recordfail gfxmode $linux_gfx_mode insmod gzio insmod part_msdos insmod ext2 set root='(hd0,msdos5)' search --no-floppy --fs-uuid --set=root &lt;uuid&gt; linux /boot/vmlinuz-3.5.0-26-generic root=&lt;uuid&gt; ro ipv6.disable=1 quirt splash $vt_handoff initrd /boot/initrd.img-3.5.0-26-generic   The  documentation says:     Boot to the recovery mode even if it is not listed on the menu:         Remove existing kernel options from the linux line and add single      But this sentence doesn't make any sense, maybe the wiki page is broken somehow. How to modify the boot menu to boot directly into recovery mode?  Note: I don't have access to grub config or anything else, only the boot menu edit page is available. I forgot my username, how do I get it back? Community user id interpreted by absolute value in search find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$ I am running Ubuntu 20.04 an  with an NVIDIA GeForce GTX 1660TI GPU. According to , the driver version for this GPU is 430. When I first installed Ubuntu, I installed 440. I'm now trying to correct that and install 430. I ran sudo apt-get install nvidia-driver-430, and then did a reboot. When I examined nvidia-smi, though, it still showed the 440: +-----------------------------------------------------------------------------+ | NVIDIA-SMI 440.100      Driver Version: 440.100      CUDA Version: 10.2     | |-------------------------------+----------------------+----------------------+ | GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC | | Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. | |===============================+======================+======================| |   0  GeForce GTX 166...  Off  | 00000000:01:00.0 Off |                  N/A | | N/A   55C    P0     9W /  N/A |      0MiB /  5944MiB |      0%      Default | +-------------------------------+----------------------+----------------------+  What is the appropriate way of updating this driver? Complex numbers equation: $z^4 = -16$ Legally possible to re-create/remake an old game? Recently I started remaking an old game on Unity. Basically I want to remake an old RPG that was released for Playstation 1. I'm not ripping anything from the old game, all the assets are being created by me. I'm creating everything from the scratch, music, 3D models, gameplay however I will keep the (copyrighted ?) names, I will try to create the characters and maps/levels as they were in the original version of Playstation 1 but with better graphics.  I'm not planning on selling it or adding in on a platform like Steam (for obvious reasons, copyrights etc), just giving it for free. But I wanna know when I will finish the development, can I share the game on public with other people so they can download it?  Can the company that made the original game sue me/fine me because of copyrights reasons even though I'm not planning on selling for money?  tl;dr Remake an non-profit game of PS1 from the scratch, can the company that holds the copyrights of the game sue me/fine me? Generating random numbers in C Does the 2020 Apple M1 MacBook Pro support 2x daisy chained Thunderbolt Displays? The Apple Silicon based  supports Thunderbolt version 3 and I'm wondering if anyone has tried connection one to an ? Of course you'd need to use one of Apple's Thunderbolt 3 to Thunderbolt 2 converters. I also understand that this version is limited to supporting only a single 4K or 6K display, but since the original Apple Thunderbolt Display is only 2K I’d want to try and daisy chain these. Can I run more than one external display from the Apple Silicon M1 CPU/GPU based MacBook Pro (or Air)? Get number of unread sms Indian passport threading coming off What do the slashes mean in the character tables? I've been reading the PF core rulebook, but confused over some of the data in the Character tables, and not found anywhere in the book that explains it, so wondering if someone could explain it?  Taking the Monk class table for example:     Level | Base Attack Bonus | ..... | Flurry of Blows Bonus      1st       |       +0          |   ....    |        -1/-1      2nd       |       +1          |   ....    |        +0/+0      ...      ...      16th  |       +12/+7/+2   |   ....    |        +14/+14/+9/+9/+4/+4/-1      17th  |       +12/+7/+2   |   ....    |        +15/+15/+10/+10/+5/+5/+0      18th  |       +13/+8/+3   |   ....    |        +16/+16/+11/+10/+6/+6/+1   What do the slashes between the bonuses mean? I am running 14.04 and have a HP Deskjet 2545 wireless printer which is supported by Ubuntu. I have run HpLIP, the latest version and installed the printer.  The printer is recognised by Ubuntu, printer and network, but LibreOffice do not see the printer. Only a Generic printer.  I don't know what to do anymore and would like to get some good advice