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HW2sol

# HW2sol - Math 55 Homework 2 Solutions 2.1 6 For each of the...

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Math 55 Homework 2 Solutions September 15, 2010 § 2.1 6. For each of the following sets, determine whether { 2 } is an element of that set. a) { 2 } 6∈ { x R | x is an integer greater than 1 } . This set contains only numbers, and no sets. b) { 2 } 6∈ { x R | x is the square of an integer } . The reason is the same as above. c) { 2 } ∈ { 2 , { 2 }} . { 2 } is explicitly included in this set. d) { 2 } ∈ {{ 2 } , {{ 2 }}} . The reason is the same as above. e) { 2 } ∈ {{ 2 } , { 2 , { 2 }}} . The reason is the same as above. f) { 2 } 6∈ {{{ 2 }}} . { 2 } . This set contains only one element: {{ 2 }} . This element is not equal to { 2 } . 8. a) True. b) True. c) False. d) True. e) True. f) True. g) False; {{∅} , {∅}} = {{∅}} , so this is not a proper subset. 21. How many elements does each set have, given a 6 = b . The cardinality | P ( S ) | = 2 | S | , as noted in § 2.1 in the text. So the solutions are: a) 2 3 = 8, b) 2 4 = 16, and c) 2 2 0 = 2. In this case, P ( P ( )) = P ( {∅} ) = {∅ , {∅}} . 28. Let A = { a,b,c } , B = { x.y } and C = { 0 , 1 } . a) A × B × C = { ( a,x, 0) , ( a,x, 1) , ( a,y, 0) , ( a,y, 1) , ( b,x, 0) , ( b,x, 1) , ( b,y, 0) , ( b,y, 1) , ( c,x, 0) , ( c,x, 1) , ( c,y, 0) , ( c,y, 1) } . 1

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HW2sol - Math 55 Homework 2 Solutions 2.1 6 For each of the...

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