Question

Need Help with Question 2.

This reading introduces you to basic ideas about the quantifiers. The two basic facts about the quantifiers you need to understand, and from which all of the logical properties of the quantifiers follow are:

Basic Fact 1: A universal quantifier (x) Fx is equivalent to an infinite conjunction: Fa & Fb & Fc & Fd & ........

where a, b, c, d, are the names of objects in the universe picked out by the 'x' in the universal quantifier '(x)'.

Basic Fact 2: An existential quantifier is equivalent to an infinite disjunction

Fa v Fb v Fc v Fd v ......

1. Expand in a two-element universe (the elements are named 'a' and 'b')

(a) ~(x) ((Fx v Gy) v Ka)

(b) (x) ~ (Kx v Ka)

(c) (Ex) (Cy v (Fx --> ~Ga))

2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Make sure you draw a vertical line underneath each variable with the letters 'F' or 'B' at the bottom of each vertical line.

You can write the wffs with the vertical lines on a piece of paper and submit a photo of it.

(a) (x) (y) (z) ((Fxy --> Gxy) v (Hxa --> Hzbu))

(b) (Ex) (Ey) Hxxy --> (z) (Gz v Hx)

(c) (z) (Ex) (y) (Axayzw v Bxycuvz)

Answer 1

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