This folder accompanies the chapter "A Little Simple Math".
It contains the following files: 

SimpleMath.tla 
   A TLA+ module that uses the TLC model checker to verify some simple
   formulas.  It explains how you can modify the file to let TLC check
   your own formulas.

SimpleMath.cfg
   A TLC configuration file needed to run TLC on the SimpleMath module.


Exercises:

Where possible, check your answers to these exercises by modifying
SimpleMath.tla and using TLC.

Note: These exercises use ASCII versions of symbols; Table 8 shows the
translation to their more familiar typeset versions.

1. Determine which of the following formulas are tautologies.

   (F => G) /\ (G => F) <=> (F <=> G)
   
   (~F /\ ~G) <=> (~F) \/ (~G)
   
   F => (F => G)
   
   (F => G) <=> (~G => ~F)

   (F => (G => H)) => ((F => G) => H) 

   (F <=> (G <=> H)) => ((F <=> G) <=> H) 
   
   (\A x : F /\ G) <=> (\A x : F)  /\ (\A x : G) 

   (\E x : F /\ G) <=> (\E x : F)  /\ (\E x : G) 
   
   (\A x : F \/ G) <=> (\A x : F)  \/ (\A x : G) 

   (\E x : F \/ G) <=> (\E x : F)  \/ (\E x : G) 
   

2. Which of the following formulas are valid for all sets S, T, and U?

   (S \subseteq T) <=> (S \cup T = T)

   (S \subseteq T) <=> \A x \in S : x \in T
   
   (S = T) <=> (S \subseteq T) /\ (T \subseteq S)

   (S \subseteq T) <=> (S \ T = {})

   (S \ T) \cup (T \ S) = (S \cup T) \ (S \cap T)

   (S \ (T \cap U)) = (S \ T) \cup (S \ U)

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Last modified on Fri Jul 27 10:18:44 PDT 2001 by lamport
