Open Question: Problem understanding domain and co domain in functions?


Hi friends,

I have some problems in maths for which I am not understanding the domain and the co domain.

a. Let A, B, C is a subset of R square. where A = { (x,y) , y=2x+1}
B = {(x,y) / y=3x}
C = {(x,y) / x-y = 7}

here in the above question what does it mean by saying “A, B, C is a subset of R square”. I do not understand the significance of R square here.

Please let me know.

Regards,
Pradeep

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Open Question: problem on proposition logic?


Hoe to solve the below problem:

An magazine states, “If I’m not watching movies, I’m
playing cricket. And if I’m not playing cricket, I’m listening to music.” We can
assume that the speaker cannot do more than one of these activities at a time. What
is the speaker doing?(Translate the given sentences into formal language; consider
the possible truth assignments.)

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How a console firmware update could make a small dent in our energy problem


Environmental groups often push for efficiency improvements in big energy hogs like cars and appliances. It’s viewed as a major way to reduce our collective energy use and carbon footprint. But a recent study argues a simple firmware update for current high definition video game consoles could provide a much easier way to chop off a small but significant portion of US residential energy usage.

The study, published by a team of Carnegie Mellon researchers in the latest issue of the journal Energy Efficiency, estimates that 100 million video game consoles sucked up nearly 16 terawatt-hours (TWh) of energy a year in the US in 2010. That’s roughly one percent of the total household energy consumption for the entire country, and nearly twice as much as all the electricity used by all homes in the state of Rhode Island.

The collective power draw for game consoles has gotten worse as those consoles have become more popular and more powerful over the years. The original PlayStation only drew a few Watts of power when being played, and the PlayStation 2 used about 79 Watts at launch (with subsequent hardware revisions becoming much more efficient). Launch units for the PlayStation 3, on the other hand, drew 180 Watts of power when playing games. That number has only come down to 100 Watts with the 2010 Slim revision.

The Xbox 360 is similarly power-hungry, using 172 Watts at launch and 94 Watts in its current Xbox 360 S incarnation. By comparison, the Wii consumes a mere 16 Watts when in active use, and a dedicated Blu-ray player draws only 20 or 30 Watts.

This increase in the consoles’ active power draw is significant in and of itself. But the real problem, according to the study, is the electricity console owners are wasting by leaving their systems idling on the dashboard menu in between play sessions. The PS3 and Xbox 360 are still drawing anywhere from 75 to 94 percent of their peak energy usage when they’re left idle like this. All that wasted electricity can add up for users that routinely decide not to turn their systems off. “For example,” the study points out, “an average user that never powers down a current model Xbox 360 will consume more than ten times the electricity as a similar user who always powers down the console after use.”

The key question, of course, is just how many people actually leave their systems running 24/7 like this in the real world. The study authors don’t attempt to determine a definitive answer. Rather, they assume that 30 percent of all console users don’t turn their systems off when they’re done. This may sound high, but it’s actually lower than the 50 percent assumption used by a similar Natural Resources Defense Council study from 2007. It also seems within the realm of reason to me, given how many of my Xbox Live friends list are listed as simply sitting on the dashboard for hours at a time at weird hours of the day.

Given that assumption, the study authors ran the numbers and found that about 68 percent of all the electricity being used by video game systems was being wasted on idle time in 2010. Console owners spent roughly $1.24 billion on that 10.8 TWh of wasted energy. The energy waste is still significant, in fact, even if you assume that only 10 percent of consoles are being left idle, rather than being turned off routinely after use.

Xbox 360 and PS3 owners could easily save a large portion of this money and energy by using the systems’ built-in automatic shutoff options, which can be set to turn the system off after as little as an hour of inactivity. These options are left off by default, though. The study assumes (rightly, I think) that few, if any, console owners are going to the trouble of digging through the menu to turn them on. If console makers were willing to push out a required firmware update that simply turned on such an automatic shutoff, the study estimates we could see a savings of 9.3 TWh of electricity usage every year, or $1.1 billion worth of energy spending. That’s not going to solve our dependence on coal power plants or anything, but it’s not nothing either.

The main hazard of flipping the auto-shutoff switch, of course, would be some unsuspecting gamers losing their unsaved progress when they leave their system unattended to go grab a quick bite to eat. The study authors concede that flipping the switch might be “a potential consumer relations hazard” for console makers, and one that could cause “pushback from consumers.” However, most games these days autosave your progress so frequently that any time lost to an inopportune shutdown would probably be minimal. Players that find the feature annoying could always turn it back off. Besides, no one said saving the environment was going to be painless.

When asked to respond to the study’s suggestion, Sony merely pointed out the PS3’s existing auto-shutoff options without directly addressing whether the company would consider updating the system’s firmware to turn them on by default. Nintendo refused to comment on the matter, and Microsoft has yet to respond. (Update: Microsoft gave Ars Technica the following statement after this story was originally published: “Xbox 360 already has a shutdown timer feature. We are always thinking of ways to achieve our sustainability goals and continue to improve upon our efforts. While we are committed to making progress on environmental concerns, we do not have any additional comment at this time.”)

It’s a shame the console makers aren’t more eager to act, because turning on these auto-shutoff features by default would be a relatively painless way to make a small but measurable impact on our collective household energy usage. “Almost all efficiency measures require years to implement on a large scale, as consumers purchase or install new technology, and most require consumers to make decisions comparing increased upfront costs with expected future savings,” the study authors write. Turning on the console’s auto-shutoff, on the other hand, “could be done with almost no upfront cost, no change in the quality and level of service provided to consumers, would have no adoption/implementation delay, and does not rely on any action or decision on the part of consumers.”

UPDATE: Since this article was first published, we’ve confirmed that new Xbox 360s currently default to shut off automatically after an hour of inactivity. The one-hour shutoff option was added to the system on top of an existing, non-default six-hour shutoff option last May, though it’s unclear whether it was set as a default for new systems at that time. Ars Technica regrets the error.

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