Since salt is an electrolyte, yes, it does cook faster, but it's not that much of a difference.
yes the salt raises the temperature to boil faster
a plain pasta is when the pasta is boiled only with salt and no sauces will be added in it.
Spaghetti will cook faster in salt water compared to plain water because the salt increases the boiling point of the water, allowing it to reach a higher temperature more quickly. This results in faster cooking times for the pasta.
Yes, actually the salt makes your water boil at a higher temperature. So instead of your water boiling at 100 degrees Celsius it boils at 110 degrees Celsius. So when you put your noodles in they cook faster. :)
It is not true.
To make it cook faster
The salt is the solute, and the water is the solvent
you fill half a pot with water, let it boil, trow as much pasta as needed, trow salt along with the pasta, (taste to check if ready) then drain the water.
To make it colder, faster.
Fresh water evaporates faster because the dissolved salts in salt water raise the boiling point by strengthening the intermolecular bonds water molecules have with each other. It's why you salt pasta water--to increasing the boiling point of the water so you can cook it at a higher temperature (and season the pasta). Adding salts also lower the freezing point of water, which is why people salt roads before snow.
Slower
Adding salt to water increases the boiling temperature, causing the water to come to a boil more slowly. This increase in the cooking temperature will, in theory, cause foods boiled in salt water to cook faster. Pure solutions will generally have lower boiling points than mixtures. Adding sugar to the water will have a similar effect but would not be nearly as nice to cook food in! Note that if pure water is heated up to a high temperature prior to the addition of the salt, the addition could cause the entire pot to start boiling suddenly. This is a result of the grains of salt acting as nucleation sites. This has the effect of making nearly-boiling water actually boil more quickly when salt is added. The tiny amount of salt required to cause a nucleation effect would have no effect on the temperature of the boiling water. In this regard, you can think of the salt as a catalyst, facilitating the change of state of the water from liquid to boiling. We said "in theory" above because adding salt to water to raise the boiling point for cooking doesn't actually work in practice. The amount of salt you'd typically add to water for cooking would have negligible effect on the boiling temperature. Let's look at some numbers. Assuming fresh water at sea level, you'd need to add 230 grams of table salt to raise the boiling point of one liter of water just 2 degrees C. To raise the boiling point of the two quarts of water you're cooking pasta your pasta in by that same two degrees, you'd have to stir in 435 grams of salt. That's well over half of an entire 737 gram blue Morton salt container! The pasta may cook faster in the hotter water, but people would probably not be coming back for second helpings of your ultra-salty linguini. Salt added to the cooking water also "hardens" the surface of the starches in pasta, reducing their stickiness. This prevents the pasta from sticking together in clumps. Somewhat counter-intuitively, oil added to boiling water does not reduce the stickiness of the pasta. It does reduce the surface tension of the water, increased by the starches in the pasta. This tends to reduce foaming. The bottom line is this: You can add a few grains of salt to pure water to kick off the boiling process with nucleation. Beyond that, add salt to water to flavor what you're cooking and to keep the pasta from sticking together. It will not have any measurable effect on cooking temperature or time.