Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

10 Questions for Assignment 10 - 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: Spring 2009;

Typology: Assignments

Pre 2010

Uploaded on 08/19/2009

koofers-user-59s
koofers-user-59s ๐Ÿ‡บ๐Ÿ‡ธ

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
HW 10 Prof. Caldwell
Due: 17 February 2009 COSC 2300
Decide whether the following are true or false. Say why or why not, in doing so, rely on
the definitions of โІand =. Remember that โˆ…is the same as {}, we use it because in some
contexts it is more readable.
Recall the formal definitions:
AโІBdef
=โˆ€x.(xโˆˆAโ‡’xโˆˆB)
A=Bdef
=โˆ€x.(xโˆˆAโ‡”xโˆˆB)
The informal interpretation of sets as kinds of sacks1in which you can put things may
help with these problems. Under the sack interpretation, the empty set is a sack containing
nothing. The set containing the empty set {{}} (or {โˆ…}) is a sack that contains an empty
sack. Membership (xโˆˆA): means you can reach into the sack Aand pull out an xโ€“
it does not mean that you can reach in an pull out a sack containing an x, but that you
actually have to be able to grab an xfrom the sack. Subset (AโІB), not to be confused
with membership, means that everything that is in the sack Ais also in the sack B,e.g. if
it is possible to pull an xout of Athen you can pull an xout of sack B.Equality: sacks A
and Bare equal if everything that is in Ais also in Band everything that is in Bis also in
A.
You might like to read what Hein has to say on pages 13-15 of chapter one which is linked
on the web-page. Ignore his claim on page 14 that {H, E, L, L, O }is not a set โ€“ otherwise
you might find it useful.
1. 1 โˆˆ {1}
2. 1 โІ {1}
3. {1} โІ {1}
4. โˆ… โˆˆ {1}
5. โˆ… โІ {1}
6. โˆ… โˆˆ โˆ…
7. โˆ… โІ โˆ…
8. {1,2} โІ {โˆ…,1,2}
9. โˆ… โˆˆ {โˆ…,1,2}
10. โˆ… โˆˆ {1,2}
11. โˆ… โˆˆ {โˆ…}
12. {โˆ…} =โˆ…
13. {{โˆ…}} =โˆ…
1The sack interpretation requires the sacks have the magical property that, if you put the same thing
into the sack more than once and then you take one of them out, theyโ€™re all gone.
1
pf2

Partial preview of the text

Download 10 Questions for Assignment 10 - Discrete Structures | COSC 2300 and more Assignments Discrete Structures and Graph Theory in PDF only on Docsity!

HW 10 Prof. Caldwell Due: 17 February 2009 COSC 2300

Decide whether the following are true or false. Say why or why not, in doing so, rely on the definitions of โІ and =. Remember that โˆ… is the same as {}, we use it because in some contexts it is more readable. Recall the formal definitions:

A โІ B def = โˆ€x.(x โˆˆ A โ‡’ x โˆˆ B) A = B def = โˆ€x.(x โˆˆ A โ‡” x โˆˆ B)

The informal interpretation of sets as kinds of sacks^1 in which you can put things may help with these problems. Under the sack interpretation, the empty set is a sack containing nothing. The set containing the empty set {{}} (or {โˆ…}) is a sack that contains an empty sack. Membership ( x โˆˆ A): means you can reach into the sack A and pull out an x โ€“ it does not mean that you can reach in an pull out a sack containing an x, but that you actually have to be able to grab an x from the sack. Subset (A โІ B), not to be confused with membership, means that everything that is in the sack A is also in the sack B, e.g. if it is possible to pull an x out of A then you can pull an x out of sack B. Equality: sacks A and B are equal if everything that is in A is also in B and everything that is in B is also in A. You might like to read what Hein has to say on pages 13-15 of chapter one which is linked on the web-page. Ignore his claim on page 14 that {H, E, L, L, O} is not a set โ€“ otherwise you might find it useful.

  1. 1 โˆˆ { 1 }
  2. 1 โІ { 1 }
  3. { 1 } โІ { 1 }
  4. โˆ… โˆˆ { 1 }
  5. โˆ… โІ { 1 }
  6. โˆ… โˆˆ โˆ…
  7. โˆ… โІ โˆ…
  8. { 1 , 2 } โІ {โˆ…, 1 , 2 }
  9. โˆ… โˆˆ {โˆ…, 1 , 2 }
  10. โˆ… โˆˆ { 1 , 2 }
  11. โˆ… โˆˆ {โˆ…}
  12. {โˆ…} = โˆ…
  13. {{โˆ…}} = โˆ… (^1) The sack interpretation requires the sacks have the magical property that, if you put the same thing

into the sack more than once and then you take one of them out, theyโ€™re all gone.