Homework1 - ST561 Fall 2010 Homework 1 Due: Monday, Oct....

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Unformatted text preview: ST561 Fall 2010 Homework 1 Due: Monday, Oct. 4th, 2010 Note: The first 4 exercises below are not to be handed in. Please make sure you can do them (and ask about them if you have questions). 1. Find the union A 1 S A 2 and intersection A 1 T A 2 of two sets A 1 and A 2 where (a) A 1 = { x : x = 1 , 2 , 3 } , A 2 = { x : x = 2 , 3 , 4 } (b) A 1 = { x : 0 < x < 1 } , A 2 = { x : 1 ≤ x < 3 } (c) A 1 = { ( x,y ) : 0 < x < 3 , < y < 3 } , A 2 = { ( x,y ) : 1 < x < 4 , 1 < y < 4 } . 2. Find S ∞ k =1 A k if (a) A k = { x : 1 /k ≤ x < 2- 1 /k } , k = 1 , 2 , 3 ,... (b) A k = { ( x,y ) : 1 /k < x 2 + y 2 ≤ 4- 1 /k } , k = 1 , 2 , 3 ,... 3. Find T ∞ k =1 A k if (a) A k = { x : 2- 1 /k < x ≤ 2 } , k = 1 , 2 , 3 ,... (b) A k = { x : 3 < x ≤ 3 + 1 /k } , k = 1 , 2 , 3 ,... (c) A k = { ( x,y ) : 0 ≤ x 2 + y 2 < 1 /k } , k = 1 , 2 , 3 ,... 4. Textbook P52, 1.3.5(iv). 5. Textbook P52, 1.3.6....
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This note was uploaded on 12/04/2010 for the course ST 561 taught by Professor Staff during the Fall '08 term at Oregon State.

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Homework1 - ST561 Fall 2010 Homework 1 Due: Monday, Oct....

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