80-211 Spring 2003

Assignment #12

Due on Wednesday,
April 23^{rd}

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 T○S, called the *composite
*(or* relational product*)* *of S and T by:

(T○S)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.