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I am looking for a concise book which explains the symbolic logic required for mathematical proofs, such as the use of quantifiers and logical connectives. Which book should I use? Thanks in advance.

Jean-Claude Arbaut
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Randy Randerson
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    Do you mean the logic symbols used in standard mathematics, or the subject of mathematical logic itself? If all you need is how to use quantifiers in proofs it wouldn't be hard to explain that. –  Apr 25 '14 at 16:02
  • The logic symbols used in standard mathematics. For example, in a recent proof I used the fact that $(x \in A) \vee (\forall X \in \mathscr{C}) x \in X \equiv (\forall X \in \mathscr{C}) [(x \in A) \vee (x \in X)]$. This step seemed valid since $(\forall X \in \mathscr{C})$ only acts on the second disjunct, but I didn't fully understand why the operation was valid. I am looking for a book that explains things like this, so I know that they are valid when they are needed in proofs. – Randy Randerson Apr 25 '14 at 16:09
  • My I humbly suggest the tutorial that comes with my proof-checking freeware. For features, testimonials, introductory video and PC-based download, visit my website at http://www.dcproof.com – Dan Christensen Apr 25 '14 at 17:42
  • "Symbolic Logic" by Graeme Forbes is very good. – Niklas Rosencrantz Apr 17 '16 at 05:23

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How about the first two chapters of Daniel J. Velleman's widely available and widely praised How to Prove It (CUP)? That covers the connectives in Ch. 1 and the use of quantifiers in Ch. 2, with lots of explanations and illustrations. (The whole book is well worth reading if you are a relative beginner at mathematics.)

Peter Smith
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