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Unformatted text preview: ELEN 303: Assignment 1 Instructor: Dr. Jean-Fran cois Chamberland Email: firstname.lastname@example.org (Subject ECEN 303) Office: Room 244F WERC Office Hours: Tue 2:30 - 3:45 p.m. Problems: 1. Following the argument presented in the notes, prove that parenleftBigg intersectiondisplay A S parenrightBigg c = uniondisplay A S c . Suppose that x belongs to (intersectiontext I S ) c . That is, there exists an I such that x is not an element of S . This implies that x belongs to S c , and therefore x uniontext I S c . Thus, we have shown that (intersectiontext I S ) c uniontext I S c . The converse is obtained by reversing the argument. Suppose that x belongs to uniontext I S c . Then, there exists an I such that x S c . This implies that x / S and, as such, x / (intersectiontext I S ) . Alternatively, we have x (intersectiontext I S ) c ....
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- Fall '07