qgis - Cutting all polygons with each other - mega slicing

Draw a big circle. Then a smaller one on top and then a smaller one and a smaller one.

You see a stack of circles like a bulls eye. If you had drawn these in QGIS the other way you would only see the largest one as it hides the others.

Is there a way in a single layer to slice every feature with every other?

Basically i have contours and i only want the band between each polygon rather than the stack of progressively bigger polys like the bulls eye example.

I have perfect data where all polygons are closed and sit perfectly inside each other.

Answer

If the contours are line feature class and are closed contour lines, as you can see below:

then you need to use lines to polygons tool from Processing toolbox -> QGIS geoalgorithoms -> Vector geometry tools -> lines to polygons

It will give you the following output, which is topologically not correct (Overlapping each other):

To modify the above topology, you need to use GRASS -> v.clean as @Klewis suggested from Processing toolbox -> GRASS GIS 7 commands -> Vector -> v.clean, and in cleaning tool use Break, as you can see below:

The output result is now topologically correct:

I selected a polygon in the above image to show you that it is a valid topology.

If the contours are already polygons in separate shapefiles, you can use difference tool repeatedly to get the difference between big polygons and smaller polygons and finally use Merge tool to put them in one polygon shapefile.