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Sample Questions for Assignment 13 - Discrete Structures | COSC 2300, Assignments of Discrete Structures and Graph Theory

Material Type: Assignment; Professor: Caldwell; Class: Discrete Structures; Subject: Computer Science; University: University of Wyoming; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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HW 13 Prof. Caldwell
Due: 26 February COSC 2300
Recall: The powerset of a set Ais written ρ(A) and is the set of all subsets of A. We
charaterized the power set by saying what it means to be an element of such a set.
xρ(A)def
=xA
1. Let A={x, y, z}and B={1,2}, write down the following sets.
a.) ρ(A) =
b.) ρ(B) =
c.) ρ() =
2. Recall, ordered pairs can be encoded as sets.
ha, bi={{a},{a, b}}
Let A={1}and B={a}, write down the elements of ρ(ρ(AB)) (there should be
16 of them) and indicate which are valid encodings of ordered pairs.
1

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HW 13 Prof. Caldwell Due: 26 February COSC 2300

Recall: The powerset of a set A is written ρ(A) and is the set of all subsets of A. We charaterized the power set by saying what it means to be an element of such a set.

x ∈ ρ(A) def = x ⊆ A

  1. Let A = {x, y, z} and B = { 1 , 2 }, write down the following sets.

a.) ρ(A) =

b.) ρ(B) =

c.) ρ(∅) =

  1. Recall, ordered pairs can be encoded as sets.

〈a, b〉 = {{a}, {a, b}}

Let A = { 1 } and B = {a}, write down the elements of ρ(ρ(A ∪ B)) (there should be 16 of them) and indicate which are valid encodings of ordered pairs.