Trying to open a VS 2012 solution (SLN file) explicitly in VS 2013 succeeds. Simply double-clicking it in Windows Explorer still opens it in VS 2012 instead.
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The .sln file indicates the intended version as one of the early lines - for example:
Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio 2013
or:
Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio 2012
However - it can only make use of this if the default application for .sln files is the "Microsoft Visual Studio Version Selector". It is not uncommon for the default .sln application to be a specific version instead. In windows 8:

you can tell which is the default because it says "keep using":

