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f2006Solns1

# f2006Solns1 - ECE 190 Fall 2006 Assignment 1 Solutions 3...

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ECE 190 — Fall, 2006 Assignment 1 Solutions 3 only A and D are equal B and C have R for their universe and - 1 B but - 1 / C E = D because 0 / E (its universe is Z + , not Z ) 4 (a) S = {- 1 , 1 } (b) T = { 0 , 2 } (c) U = — no integer is both 2 and ≤ - 2 (d) V = Z — every integer is either greater than 2 or less than 3 (e) W = — similar to (c) (f) X = Z — similar to (d) 8 (a) yes (b) no, it is an element (c) no, it is a subset (d) yes (e) yes (f) no, it is an element (g) yes (h) no (i) yes (j) yes 9 (a) A B = { 1 , 3 , 5 , 6 , 7 , 9 } (b) A B = { 3 , 9 } (c) A C = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } (d) A C = (e) A - B = { 1 , 5 , 7 } (f) B - A = { 6 } (g) B C = { 2 , 3 , 4 , 6 , 8 , 9 } (h) B C = { 6 } 10 (a) A B = { x R | 0 < x < 4 } (b) A B = { x R | 1 x 2 } (c) A c = { x R | x 0 or x > 2 } (d) A C = { x R | 0 < x 2 or 3 x < 9 } (e) A C = (f) B c = { x R | x < 1 or x 4 } (g) A c B c = { x R | x 0 or x 4 } (h) A c B c = { x R | x < 1 or x > 2 } (i) ( A B ) c = { x R | x < 1 or x > 2 } (j) ( A B ) c = { x R | x 0 or x 4 } 12 (a) true (b) false (c) false (d) false (zero is missing on the left) (e) true (f) true (g) true 1

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(h) true (i) false (the union is Q ) 15 A = { . . ., - 25 , - 20 , - 15 , - 10 , - 5 , 0 , 5 , 10 , 15 , 20 , 25 , ... } and B = { . . ., - 40 , - 20 , 0 , 20 , 40 ,. .. } B A but A B 22 (a) no — { a, d, e } ∩ { d, f } = (b) yes (c) no — { 5 , 4 } ∩ { 1 , 3 , 4 } = (d) no — 6 is not included in any of the sets (e) yes 26 (a) P ( A B ) = P ( { 2 } ) = {∅ , { 2 }} (b) P ( A ) = P ( { 1 , 2 } ) = {∅ , { 1 } , { 2 } , { 1 , 2 }} (c) P ( A B ) = P ( { 1 , 2 , 3 } ) = {∅ , { 1 } , { 2 } , { 3 } , { 1 , 2 } , { 1 , 3 } , { 2 , 3 } , { 1 , 2 , 3 }} (d) P ( A × B ) = P ( { (1 , 2) , (1 , 3) , (2 , 2) , (2 , 3) } ) = {∅ , { (1 , 2) } , { (1 , 3) } , { (2 , 2) } , { (2 , 3) } , { (1 , 2) , (1 , 3) } , { (1 , 2) , (2 , 2) } , { (1 , 2) , (2 , 3) } , { (1 , 3) , (2 , 2) } , { (1 , 3) , (2 , 3) } , { (2 , 2) , (2 , 3) } , { (1 , 2) , (1 , 3) , (2 , 2) } , { (1 , 2) , (1 , 3) , (2 , 3) } , { (1 , 2) , (2 , 2) , (2 , 3) } , { (1 , 3) , (2 , 2) , (2 , 3) } , { (1 , 2) , (1 , 3) , (2 , 2) , (2 , 3) }} 28 (a) P ( ) = {∅} (b)
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f2006Solns1 - ECE 190 Fall 2006 Assignment 1 Solutions 3...

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