title: Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series)
author:  D.L. Johnson 
description: From the reviews: It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence.  This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course. (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)
zlib_text: Language and Proofs in Algebra: An Introduction
  Version 1.0
  c� Faculty of Mathematics, University of Waterloo
  August 9, 2018
  
  Contents
  1
  Introduction to the Language of Mathematics
  6
  1.1
  The Language
  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
  6
  1.2
  Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
  7
  1.3
  Mathematical Statements and Negation . . . . . . . . . . . . . . . . . . . .
  8
  1.4
  Quantiﬁers and Quantiﬁed Statements . . . . . . . . . . . . . . . . . . . . .
  10
  1.4.1 Universal and Existential Quantiﬁers
  . . . . . . . . . . . . . . . . . .
  10
  1.4.2 Quantiﬁers and Language . . . . . . . . . . . . . . . . . . . . . . . . .
  12
  1.4.3 Negation of Quantiﬁers . . . . . . . . . . . . . . . . . . . . . . . . . .
  13
  1.5
  Nested Quantiﬁers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
  14
  1.5.1 Two Quantiﬁers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
  14
  1.5.2 An Arbitrary Number of Quantiﬁers . . . . .