- 10 The Notion Of Statement Form Also Called Well Formed Formula Can Be Described More Carefully Than In The Text Sta 1 (127.13 KiB) Viewed 18 times
- 10 The Notion Of Statement Form Also Called Well Formed Formula Can Be Described More Carefully Than In The Text Sta 2 (31.45 KiB) Viewed 18 times
10. The notion of
statement form (also called well-formed formula) can be described more carefully than in the text. Start with a collection of sym- bols that we agree to call
statement letters. (Do not allow the symbols ), (, ~, V, 1, 3, 4 to be in this collection. A
statement letter is a
statement form of the simplest kind; and if S1 and S2 are
statement forms, then so are ~ (Si), (Si) V (S2), (Si) 1 (S2), (Si) = (S2), and (Si) 4 (S2). Parentheses may be omitted when confusion is unlikely. [But they are sometimes essential; if Sį is P = Q and S2 is Q = R, then Si = S2 is written (P GQ) (Q = R).] Taking our usual alphabet as the collection of
statement letters, determine which of the following are
statement forms. In each case when the given expression is not a
statement form, insert parentheses so that it becomes such a form.
(a) (PB-Q) ((~(~ P)) #Q) (b) (P =Q3R) SBT ) ) (c) (P ~(~ R)) = Q R (d) (( PQ R) AQ) V (~(P VQ)) (e) (~ PVQ) A (((PAQ) V (PAR)) = (SV ~ P)) () ν ()) = . Q =