<p>Symbolic Logic I Study Guide and Worksheet</p><p>Logical Syntax Logic, like ordinary language, has a syntax, a set of rules determining which strings of symbols are meaningful within a particular language. When a string of symbols satisfies the syntax rules, that string is said to be well-formed. In logic well-formed formulas are called WFF's (pronounced "woofs"). It is important to be able to separate out WFF's from strings of symbols that are syntactically incorrect. Below are several definitions and the rules of logical syntax, the rules of WFF formation.</p><p>Definitions: 'Statement Letter' -- Any capital letter used to symbolize a simple statement 'Connective' -- a tilde (~), dot (), wedge (), arrow (), or double arrow () 'Grouper' -- a parenthesis, bracket, brace, etc. 'Symbol' -- a statement letter, connective, or grouper 'Formula' -- any horizontal string of symbols 'Left-hand grouper' -- a '(', '[', or '{' 'Matching right-hand grouper -- the mirror image of a left-hand grouper 'Binary Connective' -- any connective other than a tilde</p><p>With these definitions we can now define a WFF A WFF is either (a) a statement letter (b) a tilde followed by a WFF, (c) a left-hand grouper followed by a WFF followed by a binary connective followed by a WFF followed by a matching right-hand grouper*</p><p>EXERCISES Using the definitions given above, determine which of the following formulas are WFF's</p><p>1) (~A  B) 2) ~(C  ~~~D) 3) (E ~F) 4) (G  H  I) 5) {[(A  B)  F]  (G  H)} 6) A  [(B  ~C)  D] 7) A  [(B  ~) C  D] 8) (A  ) [B  C )  ~D] 9) {J  ~[(K  L)  M]} 10) PQ  (R~S)</p><p>*We will, for the sake of simplicity, allow a formula which would be a WFF under (c) if the formula were encased in a set of parentheses to count as a WFF. So, while 'A  B' is not, technically speaking, a WFF we will treat it as one since (A  B) is a WFF. We shall act as if the outermost set of parentheses were present.</p>