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2020-03-09

Practice Midterm Solutions Discussion.

  Gricelda Tecun, Michael Kang, Keven Lam

1. Define the following set theory concepts: (a) one set is a subset of another (define using ∈), (b) ordered pair (a,b) (define as a set), (c) partition of sets.

a) A ⊆ B := ∀x(x∈A ⇒ x∈B)

b) (a, b) := {a, {a, b}}

c) Given subsets S1, S2, ... Sn of S, if:

   1. S1 ∪ S2 ∪ ... ∪ Sn = S
   2. For each i and j, Si ∩ Sj = ∅
   3. For each i, Si ≠ ∅

(Edited: 2020-03-09)

Gricelda Tecun, Michael Kang, Keven Lam 1. Define the following set theory concepts: (a) one set is a subset of another (define using ∈), (b) ordered pair (a,b) (define as a set), (c) partition of sets. a) A ⊆ B := ∀x(x∈A ⇒ x∈B) b) (a, b) := {a, {a, b}} c) Given subsets S1, S2, ... Sn of S, if: 1. S1 ∪ S2 ∪ ... ∪ Sn = S 2. For each i and j, Si ∩ Sj = ∅ 3. For each i, Si ≠ ∅

-- Practice Midterm Solutions Discussion

Group members: Phuc Phan, Rayyan Khan, Prajesh Shrestha
Problem 3
check reflexive: (a,b) ~ (a,b) because a.b = c.d
check symmetric: if (a,b) ~ (c,d) which means a.b = c.d -> c.d = a.b -> (c,d)~(a,b)
check transitive: if(a,b) ~(c,d) and (c,d)~(e,f) which means a.b = c.d and c.d = e.f -> a.b = e.f -> (a,b)~(e,f)
Conclude: ~ is an equivalence relation

(Edited: 2020-03-12)

* Group members: Phuc Phan, Rayyan Khan, Prajesh Shrestha * Problem 3 * check reflexive: (a,b) ~ (a,b) because a.b = c.d * check symmetric: if (a,b) ~ (c,d) which means a.b = c.d -> c.d = a.b -> (c,d)~(a,b) * check transitive: if(a,b) ~(c,d) and (c,d)~(e,f) which means a.b = c.d and c.d = e.f -> a.b = e.f -> (a,b)~(e,f) * Conclude: ~ is an equivalence relation

-- Practice Midterm Solutions Discussion

Question #10 Group: Jonathan Wong, Nick Fulton, Dillon Larson, Tyler Wasniowski, Hamir Mahal Resource Description for Midterm#10.pdf If the image doesn't load, use this Google Drive

(Edited: 2020-03-09)

Question #10 Group: Jonathan Wong, Nick Fulton, Dillon Larson, Tyler Wasniowski, Hamir Mahal ((resource:Midterm#10.pdf|Resource Description for Midterm#10.pdf)) If the image doesn't load, use this [[https://drive.google.com/file/d/1sX82p567nQiQdqmJUBNRUX54ITcGb0Es/view?usp=sharing|Google Drive]]

-- Practice Midterm Solutions Discussion

Problem #6

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Problem #6 ((resource:Note Mar 9, 2020 (2).jpg|Resource Description for Note Mar 9, 2020 (2).jpg))

-- Practice Midterm Solutions Discussion

Problem 5 - Sebrianne, johanna, Zhijie Xu

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(Edited: 2020-03-09)

Problem 5 - Sebrianne, johanna, Zhijie Xu ((resource:Snapchat-852008844.jpg|Resource Description for Snapchat-852008844.jpg)) ((resource:Snapchat-1322908080.jpg|Resource Description for Snapchat-1322908080.jpg))

-- Practice Midterm Solutions Discussion

Problem #7 group: Jinyin Chai, Lichun Gao, Jieni yan

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(Edited: 2020-03-09)

Problem #7 group: Jinyin Chai, Lichun Gao, Jieni yan ((resource:WechatIMG60.png|Resource Description for WechatIMG60.png))

-- Practice Midterm Solutions Discussion

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(Edited: 2020-03-09)

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-- Practice Midterm Solutions Discussion

Question 9: Sumaiyya Burney, Joshua Harmon, Max Garcia, Sandeep Isher, Gurseerat Singh, Holly Lind

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Since NextStates does not contain an accept state after traversing the entire string, 001101 is NOT in the language

(Edited: 2020-03-09)

Question 9: Sumaiyya Burney, Joshua Harmon, Max Garcia, Sandeep Isher, Gurseerat Singh, Holly Lind ((resource:9.png|Resource Description for 9.png)) Since NextStates does not contain an accept state after traversing the entire string, 001101 is NOT in the language

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