80-211 Spring 2003

 

Assignment #12

Due on Wednesday, April 23rd

 

Problem 1: Do problems 2 and 3 on pages 187-8 of your text.

 

Problem 2: Given any two relations S and T, one defines a new relation TS, called the composite (or relational product) of S and T by:

 

(TS)xy =df ($z)(Sxz & Tzy)

 

A relation R is said to be functional if it satisfies the conditions:

 

(i) (x)( $y) Rxy

(ii) (x)(y)(z) [(Rxy & Rxz) (y=z)]

 

Using predicate calculus with equality, show that the composite of two functional relations is again functional.