hw1solsmc - Solutions to Homework 1 - Math 2000 Notes: I...

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Solutions to Homework 1 - Math 2000 Notes: I have removed 1.12(b) from the list. (# 1.4. (b),(d)) Write each of the following sets by listing its elements within braces. ( b ) . B = { n Z | n 2 < 5 } ( d ) . D = { x Z | x 2 - x = 0 } Solution . (b). Note that n 2 < 5 only if n 2 < 5 = 2 . 236 ... (by a calculator computation). However, n 2 = | n | . Therefore this identity is equivalent to | n | < 2 . 236 .... This says that - 2 . 236 ... < n < 2 . 236 .... The only integer solutions are n = - 2 , - 1 , 0 , 1 , 2. Hence B = {- 2 , - 1 , 0 , 1 , 2 } . (d). Note that x 2 - x = 0 factors as follows: 0 = x 2 - x = x ( x - 1) . This equals zero only if x = 0 or x = 1. Therefore D = { 0 , 1 } . (# 1.6) For the following sets describe the set by listing its elements: ( a ) . A = { 2 x + 1 | x Z } ( b ) . B = { 4 n | n Z } ( c ) . C = { 3 q + 1 | q Z } Solution . (a). Since Z is the integers we just take a few small values, say x = - 2 , - 1 , 0 , 1 , 2. We find that 2( - 2) + 1 =
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This note was uploaded on 11/08/2009 for the course MATH 2000 taught by Professor Dd during the Spring '09 term at District of Columbia.

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hw1solsmc - Solutions to Homework 1 - Math 2000 Notes: I...

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