Quiz 3 Quiz 3                              Friday, March 30, 2001



NAME:

Student Number:------            No.----           Marks ----






(25 Marks)    Let A and B be two sets. Prove that



AB
 
=
A
 

B
 
.
Proof. (i) We prove that [`(AB)] [`A][`B]. In fact, let x [`(AB)]. Then x AB. This implies x A or x B. Hence, x [`A] or x [`B], that is, x [`A][`B].

(ii) We prove that [`A][`B] [`(AB)]. Since AB A and AB B, we have



A
 

AB
 
   and
B
 

AB
 
.

This implies [`A][`B][`(AB)].

By (i) and (ii), we obtain [`(AB)] = [`A][`B].




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On 3 Apr 2001, 10:18.