Professor Kate Poirier, Spring 2017

# Month: February 2017(Page 1 of 3)

The first in-class test will be given on Thursday, March 9. It will cover material/homework from Sections 1.1, 1.3, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, and 2.3. The test will take up the first 60 minutes of class time. The remaining time will be used for a shortened lesson.

Quiz #3 will be given in class this Thursday, March 2. It will cover material/homework from Section 1.7.

Here is a photo of the board from the end of the lesson on nested quantifiers. Part of our discussion was a little rushed, so I wanted to recap here.

Recall that $T(x,y)$ means that student $x$ likes cuisine $y$. Recall also that the names $x$ and $y$ don’t matter…what matters is that the first entry is always a student and the second entry is always a cuisine. The exercise was to translate the propositions below into English sentences.

(a) $\neg T(Juliano, Japanese)$ translates to “Juliano does not like Japanese food.”

(b) $\exists x T(x, Korean) \wedge \forall x T(x, Mexican)$ translates to “There is a student who likes Korean food and all students like Mexican food.

(c) $\exists y (T(Shannon, y) \vee T(Jiayu, y))$ translates to “There exits a cuisine that either Shannon or Jiayu (or both) like.”

(d) $(x \neq z) \rightarrow \neg (T(x,y) \wedge T(z,y)))$…let’s do this translation in a few steps:

• $T(x,y) \wedge T(z,y)$ translates to “Students x and z like cuisine y.”
• $\neg (T(x,y) \wedge T(z,y)$ translates to “It is not the case that students x and z like cuisine y,” which we can translate to “Either student x or student z does not like cuisine y.”
• $(x \neq z) \rightarrow \neg (T(x,y) \wedge T(z,y)))$ translates to “If x and z are different students, then either student x or student z does not like cuisine y.”
• So far none of the statements are propositions, since we don’t know the values of the variables, but we can turn the last statement into a proposition by adding the quantifiers. $\forall x \forall z \exists y ( (x \neq z) \rightarrow \neg (T(x,y) \wedge T(z,y)))$ translates to “For all students x and students z there exists a cuisine y such that if x and z are different students, then either student x or student z does not like cuisine y.” We can translate this into a more natural sentence in English by eliminating the variables: “For any pair of two distinct students, there is a cuisine that one of the students does not like.”

(e) $\exists x \exists z \forall y (T(x,y) \leftrightarrow T(z,y))$…again, let’s do this translation in a few steps:

• $T(x,y) \leftrightarrow T(z,y)$ translates to “Student x likes cuisine y if and only if student z likes cuisine y.”
• Again, the above statement is not a proposition since we don’t know the values of the variables, but we can upgrade it to a proposition by adding the quantifiers. $\exists x \exists z \forall y (T(x,y) \leftrightarrow T(z,y))$ translates to “There exists a student x such that there exists a student z such that for all cuisines y, student x likes cuisine y if and only if student z likes cuisine y.” We can translate this into a more natural sentence in English: “There exits a pair of two students who like all the same cuisines as one another and don’t like all the same cuisines as one another.

(f) $\forall x \forall z \exists y (T(x,y) \leftrightarrow T(z,y))$…let’s do this translation in a few steps:

• $T(x,y) \leftrightarrow T(z,y)$ is the same as in question (e)
• This time the quantifiers will change the statement to: “For all students x and for all students z there exists a cuisine y such that student x likes cuisine y if and only if student z likes cuisine y.” Again, we translate this into a more natural sentence: “For all pairs of students there is a cuisine that they either both like or both do not like.”
1. Quiz #2 on Thursday, February 23 will cover material/homework from sections 1.4, 1.5, and 1.6.
2. For section 1.6, the homework questions are #4, #10, #19, #20, and #35. I will change the calendar to reflect this, but the course outline will not be updated.
3. For 1.6 #3 (done by you and your partner in class today) you can check the back of the text to make sure your answers are correct. If you have any questions, you can post them here on the OpenLab or ask them in my office hours on Tuesday 11am-1pm.

Hello to everyone. I started my journey from Queensborough Community College. I finished my associates in the field of computer information systems. Then I transferred to New York City College of Technology to finish my bachelor’s in computer systems and technology. So far it’s my third semester here. I have been to USA for about four years. I am from Bangladesh. I am really glad to be a part of this class. The class seems really exciting and active. I hope I can learn something from this class.

Hello, my fellow peers my name is Shah Nawaz and It’s my third year here at City Tech, which means i’ll be graduating soon. I just got into computers just for the fun of it because i been interested in computers for a long time since i was in middle school.At home i be opening computers and cleaning them from inside and just i am amazed the amount of technology that goes into a small device such as a laptop. After graduating i hope to find a good job in the computer related field although i don’t have short term or long term goals yet but still i hope to pass college and at least a bachelor’s degree. I hope to gain a lot of knowledge from this course and how algorithms play a role in our daily life. My hobbies include playing pool and basketball. Bye Now hope to see you soon – peers!!!!

Hi my name is Joshua Morton and I am currently majoring in computer systems, specifically the software development track.  I am looking to develop my skills in coding and understand techniques in applying algorithms to my future coding projects.  I want to be a game developer in the near future.  My goal is the creation of my own gaming studio with friends while i’m here in college to start our business.  Other than that, some of my hobbies included video gaming, video gaming, and video gaming. (sorry for the late post)

Hello everyone I am Fuad shalek. My major is Computer System Technology. When i was younger my cousin introduced me to computers. After that I became really interested in it and wanted to learn more about how it  operates.  My hope after I graduate is to find an entry level job in my field that will allow me to have enough financial stability to allow me to further my education.  From this class I want to gain an understanding of how the algorithm and discrete mathematics are used in programming. My other interest are video games and PC building.

Hello

I’m a transfer student and this is my second semester here at City Tech. My major is in computer systems focusing on networking and security. I started doing programming, but wasn’t as enthusiastic about it and switched over to network where I’m enjoying it more. I’ve always been into computers since my dad worked in the field doing networking, so I was exposed to it at an early age.  I’ve already learned a lot about this field from him making it an easy decision when selecting my major. After graduating from here, I hope to work in the networking field as a network administrator. If that doesn’t work out, the security field is also very good. I hope to fully understand algorithms and mathematical logic since it is the bases of computer programming, at the end of the semester. During my free time, I like working on computers and building them. I’ve built many for friends and family so they can have a better computer and not spend so much on it. I also enjoy writing programs for fun. It helps me get better at coding and I just find it fun.