Had you not includedDiscrete Mathematics, without a doubt I would suggestSet Theoryby Charles Pinter.

Pinter did his PhD in Paris in the 1960's with some of the leading reformers of mathematics notation.

IfDiscrete Mathematicsis a must for you thenDiscrete Mathematicsby Richard Johnsonbaugh is a good choice.

The first is a more in depth study of the basics; the second is a study of more topics but in less depth.