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# homework1 - CSE 105 HOMEWORK 1 SOLUTIONS prepared by...

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CSE 105 - HOMEWORK 1 SOLUTIONS prepared by Lawrence Cayton 0.1 a. Odd natural numbers b. Even integers c. Even natural numbers d. Even natural numbers that are multiples of 3 e. Symmetric binary numbers f. The empty set 0.2 a. { 1 , 10 , 100 } b. { x ∈ Z| x > 5 } c. { x ∈ N| x < 5 } d. { aba } e. { } f. 0.3 a. No: A B b. Yes: B A c. A B = { x, y, z } d. A B = { x, y } e. A × B = { ( x, x ) , ( x, y ) , ( y, x ) , ( y, y ) , ( z, x ) , ( z, y ) } f. P ( B ) = {∅ , { x } , { y } , { x, y }} 0.4 Each element of A is paired with each element of B , so | A × B | = ab . 0.5 There are 2 c elements in the powerset of C . Suppose we label each element of C with a 1 or 0 and form the subset of elements of C that we labelled with a 1. Then, we can describe each element of the powerset – any subset of C – this way, so the size of the powerset is the number of 0-1 labellings of the elements of C . 0.6 a. 7 b. range ( f ) = { 6 , 7 } , domain ( f ) = { 1 , 2 , 3 , 4 , 5 } c. 6 d. range ( g ) = { 6 , 7 , 8 , 9 , 10 } , domain ( g ) = { ( x, y ) ∈ N × N| 1 x 5 , 6 y 10 } e. g (4 , f (4)) = g (4 , 7) = 8 0.7 Each of the following relations is defined over A = { a, b, c } a. { ( a, a ) , ( b, b ) , ( c, c ) , ( a, b ) , ( b, a ) , ( b, c ) , ( c, b ) } ; since ( a, c )

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homework1 - CSE 105 HOMEWORK 1 SOLUTIONS prepared by...

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