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.