Assignment1(1804)(Solution)

Assignment1(1804)(Solution) - MATH 1804 University...

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Unformatted text preview: MATH 1804 University Mathematics A Assignment 1 – Solution January 25, 2011 1. (Generally speaking, there are a lot of possible ways to describe the same set with the set-builder notation. Here we suggest a few natural answers. Each has its own advantages.) (a) { n ∈ Z : n < , n is odd } OR { 1- 2 n : n ∈ N } OR {- n : n ∈ N , n is odd } (b) { n 2 : n is even } OR { 4 n 2 : n ∈ Z } OR { 4 n 2 : n ∈ N ∪ { }} OR { 4( n- 1) 2 : n ∈ N } (c) { x ∈ R : 2 < √ x < 10 } OR { x ∈ R : 4 < x < 100 } Remark on 1. If set-builder notation is not required, there could be other natural ways to describe these sets; for instance, (4 , 100) in (c). 2. (a) { 2 } (b) { 2 5 , 2 } 3. (a) {- 6 , 3 } (b) ∅ (c) (- 10 ,- 2) Remark on 3. (complex solutions) (b) We have restricted to real solutions. But if one accepts complex solutions, then the answer of (b) should of course be { 2 3 ± i √ 17 3 } . This course is interested in real numbers only, thus sets of numbers are by default the real ones. (c) Though not required by this course, it is interesting enough to mention that (c) does have complex solutions {- 6 + iy : y ∈ R } ∪ (- 10 ,- 2)....
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This note was uploaded on 04/19/2011 for the course MATH 1804 taught by Professor Ng during the Spring '11 term at HKU.

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Assignment1(1804)(Solution) - MATH 1804 University...

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