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# 131A1SOL - Online EE 131A 1 a S = cfw_1 2 3 4 5 6 b A =...

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Online EE 131A Homework #1 Fall 2010 Solution K. Yao 1. a. S = { 1 , 2 , 3 , 4 , 5 , 6 } . b. A = { 2 , 4 , 6 } . c. A c = { 1 , 3 , 5 } ≈ “odd number of dots.” 2. a. S = set of ordered pairs ( x, y ) where x, y ∈ { 1 , 2 , 3 , 4 , 5 , 6 } . 1 2 3 4 5 6 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) b. { (1 , 1) , (2 , 2) , (3 , 3) , (4 , 4) , (5 , 5) , (6 , 6) } . c. { (1 , 1) , (1 , 2) , (2 , 1) , (2 , 3) , (3 , 2) , (1 , 4) , (4 , 1) , (6 , 1) , (1 , 6) , (5 , 2) , (2 , 5) , (3 , 4) , (4 , 3) , (5 , 6) , (6 , 5) } . 3. i. S = { ( g 1 , g 2 ) , ( g 1 , g 3 ) , ( g 1 , d 1 ) , ( g 1 , d 2 ) , ( g 2 , g 1 ) , ( g 2 , g 3 )( g 2 , d 1 ) , ( g 2 , d 2 ) , ( g 3 , g 1 ) , ( g 3 , g 2 ) , ( g 3 , d 1 ) , ( g 3 , d 2 ) , ( d 1 , g 1 ) , ( d 1 , g 2 )( d 1 , g 3 ) , ( d 1 , d 2 ) , ( d 2 , g 1 ) , ( d 2 , g 2 ) , ( d 2 , g 3 ) , ( d 2 , d 1 ) } ii. a. E 1 = { ( g 1 , d 1 ) , ( g 1 , d 2 ) , ( g 2 , d 1 ) , ( g 2 , d 2 ) , ( g 3 , d 1 ) , ( g 3 , d 2 ) , ( d 1 , g 1 ) , ( d 1 , g 2 ) , ( d 1 , g 3 ) , ( d 2 , g 1 ) , ( d 2 , g 2 ) , ( d 2 , g 3 ) } . b. E 2 = S - { ( d 1 , d 2 ) , ( d 2 , d 1 ) } . c. E 3 = { ( g 1 , d 1 ) , ( g 1 , d 2 ) , ( g 2 , d 1 ) , ( g 2 , d 2 ) , ( g 3 , d 1 ) , ( g 3 , d 2 ) , ( d 1 , g 1 ) , ( d 1 , g 2 ) , ( d 1 , g 3 ) , ( d 1 , d 2 ) , ( d 2 , g 1 ) , ( d 2 , g 2 ) , ( d 2 , g 3 ) , ( d 2 , d 1 ) } , or E 3 = S - { ( g 1 , g 2 ) , ( g 1 , g 3 ) , ( g 2 , g 1 ) , ( g 2 , g 3 ) , ( g 3 , g 1 ) , ( g 3 , g 2 ) } . d. E 4 = { ( d 1 , d 2 ) , ( d 2 , d 1 ) } 4. a. S = { (1 , 2 , 3) , (2 , 1 , 3) , (3 , 1 , 2) , (1 , 3 , 2) , (2 , 3 , 1) , (3 , 2 , 1) } b. A 1 = { (1 , 2 , 3) , (1 , 3 , 2) } , A 2 = { (1 , 2 , 3) , (3 , 2 , 1) } , A 3 = { (1 , 2 , 3) , (2 , 1 , 3) } .

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