The English Channel is the body of water between England (Great Britain) and France, it is connected to the Atlantic Ocean.
Being a body of water, it can't be a water way - so the answer b) is false.
In fact, from the description above you know that the answer a. an extension of the Atlantic Ocean between England and France is true.
The false statement is - B. This map projection does not distort shapes.
The map shown on the image is a Mollweide projection map. This is a map that has an elliptical shape, unlike most of the maps that have a rectangular shape. It is a map that pretty accurately manages to depict the Earth's continents with their right sizes.
Unfortunately, it can not be said that the map is without flaws. It is a map that has distortions, as all the others do, but it is still a map where the distortions are very small, thus the depiction is much accurate than on most of the other map projections.
I think water and food is something that's encouraged people to settle where I live.