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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
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This note was uploaded on 04/10/2008 for the course CSE 105 taught by Professor Paturi during the Fall '99 term at UCSD.

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

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