hw2 - SOLUTIONS FOR HOMEWORK 2 1.51. (a) Yes , I f ( X Y )...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SOLUTIONS FOR HOMEWORK 2 1.51. (a) Yes , I f ( X Y ) = I f ( X ) I f ( Y ). To establish this equality, note that a I f ( X Y ) iff f ( a ) X Y . The last equality holds when either f ( a ) X , or f ( a ) Y . By the definition of I f , f ( a ) X is equivalent to a I f ( X ), and similarly, f ( a ) Y is equivalent to a I f ( Y ). Thus, f ( a ) X Y iff a I f ( X ) I f ( Y ). (b) Yes , I f ( X Y ) = I f ( X ) I f ( Y ). Indeed, a I f ( X Y ) iff f ( a ) X Y , that is, f ( a ) X , and f ( a ) Y . As noted in (a), f ( a ) X iff a I f ( X ), and f ( a ) Y iff a I f ( Y ). Thus, f ( a ) X Y iff a I f ( X ) I f ( Y ). 1.55. Multiplication. Show first that x x = 0, or equivalently, x = x- 1 . By Definition 1.39, x has the opposite element x- 1 = y F s.t. x y = 0. We have to show that y = x , or in other words, y negationslash = 0, and y negationslash = 1. However, these cases are easy to rule out: x 0 = 0 negationslash = 1, and x 1 = x negationslash = 1. The only remaining possibility is= 1....
View Full Document

This note was uploaded on 01/27/2010 for the course MATH 347 taught by Professor ? during the Fall '09 term at University of Illinois at Urbana–Champaign.

Page1 / 2

hw2 - SOLUTIONS FOR HOMEWORK 2 1.51. (a) Yes , I f ( X Y )...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online