Symbolic Logic I

Statement Forms and Substitution Instances

Every WFF is a substitution instance of a statement form.  Here are two lists, one of statement forms, the other of WFF’s.  Identify each of the statement forms of which each WFF is an instance, remembering that a WFF may be a substitution instance of more than one statement form.

 Statement Forms WFF’s a.                   p b.                  ~p c.                   p ▼ q d.                  p → q e.                   ~(p → q) f.                    ~p → q g.                   ~p → (q ▼ r) h.                   (p ▼ q) → r i.                     p · q j.                    ~(p · q) k.                  ~p · (q ▼ r) 1.         A → B 2.                  P → (Q ▼ R) 3.                  ~P → (Q ▼ R) 4.                  P ▼ (Q → R) 5.                  ~[(P · Q) · R] 6.                  (P ▼ Q) → (R · ~S) 7.                  ~P · (Q → R) 8.                  P · (Q ▼ R) 9.                  {[P « (Q ▼ S)] · R} · P 10.              ~(Q ▼ R) → ~(R · S) 11.              {[P · (Q · S)] · R} · P 12.              ~(P · Q) · R 13.              ~[P → (Q ▼ R)] 14.              ~[~P → (Q ▼ R)]