Question

1. Expand in a two-object universe (the objects are named 'a' and 'b') (a) (Ex) ((Ax \supset Bd) = Dy) (b) ~ (x) ~ (Ax & Cz) (c) (x) ~ (Dy \supset (Hx & ~Ga)) Expanding a wff is not the same as reducing the wff to conjunctive normal form (or reducing it to disjunctive normal form). Read the text and my handout on how to do an expansion. 2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Either (i) draw a vertical line underneath each variable with the letters 'F' or 'B' at the bottom of each vertical line or (ii) color bound variables red and free variables green. Make sure you know which symbols are used for variables. Not every symbol in the language of predicate logic is used for variables. The reading (Scope, binding, and quantifier expansions) lists the symbols that are used for variables and the symbols that used for the names of objects (i.e., individual constants). Names of objects are not names of variables. The free/bound distinction only applies to variables. It does not apply to individual constants (i.e., names of objects) (a) (x) (y) (Ez) ((Ayzxv \supset Bzzy) v (Fxac \supset Hzauzu)) (b) (Ex) (Ey) Hyabwa \supset (z) (Fzvhky v Hxyyx) (c) (z) (Ex) (y) (Axyzyyw v Bxyxzavz)

          1. Expand in a two-object universe (the objects are named 'a' and 'b')
(a) (Ex) ((Ax \supset Bd) = Dy)
(b) ~ (x) ~ (Ax & Cz)
(c) (x) ~ (Dy \supset (Hx & ~Ga))
Expanding a wff is not the same as reducing the wff to conjunctive normal form (or reducing it to disjunctive normal form). Read the text and my handout on how to do an expansion.
2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Either (i) draw a vertical line underneath each variable with the
letters 'F' or 'B' at the bottom of each vertical line or (ii) color bound variables red and free variables green. Make sure you know which symbols are used for variables. Not every symbol in
the language of predicate logic is used for variables. The reading (Scope, binding, and quantifier expansions) lists the symbols that are used for variables and the symbols that used for the
names of objects (i.e., individual constants). Names of objects are not names of variables. The free/bound distinction only applies to variables. It does not apply to individual constants (i.e.,
names of objects)
(a) (x) (y) (Ez) ((Ayzxv \supset Bzzy) v (Fxac \supset Hzauzu))
(b) (Ex) (Ey) Hyabwa \supset (z) (Fzvhky v Hxyyx)
(c) (z) (Ex) (y) (Axyzyyw v Bxyxzavz)

1. Expand in a two-object universe (the objects are named 'a' and 'b')
(a) (Ex) ((Ax ⊃Bd) = Dy)
(b) (x) (Ax Cz)
(c) (x) (Dy ⊃(Hx Ga))
Expanding a wff is not the same as reducing the wff to conjunctive normal form (or reducing it to disjunctive normal form). Read the text and my handout on how to do an expansion.
2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Either (i) draw a vertical line underneath each variable with the
letters 'F' or 'B' at the bottom of each vertical line or (ii) color bound variables red and free variables green. Make sure you know which symbols are used for variables. Not every symbol in
the language of predicate logic is used for variables. The reading (Scope, binding, and quantifier expansions) lists the symbols that are used for variables and the symbols that used for the
names of objects (i.e., individual constants). Names of objects are not names of variables. The free/bound distinction only applies to variables. It does not apply to individual constants (i.e.,
names of objects)
(a) (x) (y) (Ez) ((Ayzxv ⊃Bzzy) v (Fxac ⊃Hzauzu))
(b) (Ex) (Ey) Hyabwa ⊃(z) (Fzvhky v Hxyyx)
(c) (z) (Ex) (y) (Axyzyyw v Bxyxzavz)

Added by Melissa P.

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