CPSC 121 2021S2
HW 3
Solutions
Instructions:
1. Do not change the problem statements we are giving you. Simply add your
solutions by editing this latex document. To make it easier for the TAs to find
your solutions, please use the soln environment we provided as follows:
\begin{soln}
My solution is here.
\end{soln}
Your solution will then appear in blue, and be easier to differentiate from the
questions.
2. If you need more space, add a page between the existing pages using the
\newpage command.
3. Export the completed assignment as a PDF file for upload to gradescope.
4. On Gradescope, upload only one copy per partnership. You must identify
you group via Gradescope, not doing so may result in loosing some marks
5. You must also tell us, via Gradescope, where each of the problem parts
appears on your submission. You MUST align the regions for every problem,
even if your assignment solution isn’t complete. We will not be able to mark
any problem we can’t find. After uploading the .pdf you will a screen, where
you can click each question on the left, and click the corresponding page(s) for
which the question appears in. Because of this matching process, please allocate
at least 5 minutes prior to the deadline for submission. You must match your
answers with each question, not doing so may result in loosing some marks.
Academic Conduct: I certify that my assignment follows the academic
conduct rules for of CPSC 121 as outlined on the course website. As part of
those rules, when collaborating with anyone outside my group, (1) I and my
collaborators took no record but names away, and (2) after a suitable break,
my group created the assignment I am submitting without help from anyone
other than the course staff.
1
, CPSC 121 2021S2
1. [6 marks] Given the following definitions:
• S: the domain of all CPSC 121 students.
• G: the domain of all graded CPSC 121 activities.
• A(x, y): student x earns an “A” grade on activity y
• B(x): student x receives a colourful balloon (from the CPSC 121 teaching team).
Now consider the predicate logic statements:
Statement 01: ∀x ∈ S, ∀g ∈ G, A(x, g) ↔ B(x)
Statement 02: ∀x ∈ S, (∀g ∈ G, A(x, g)) ↔ B(x)
Statement 03: ∀x ∈ S, (∀g ∈ G, (∀y ∈ S, A(y, g))) ↔ B(x)
Describe how these statements differ, in terms of who receives a balloon and under what
conditions.
For statement 01, any number of students can receive balloons, and balloons are earned
per activity.
For statement 02, any number of students can receive balloons, but only one balloon can
be awarded when the student aces the entire course.
For statement 03, either nobody gets a balloon, or everybody gets a balloon. The balloons
are awarded if everyone in the class aces the entire course together.
2
HW 3
Solutions
Instructions:
1. Do not change the problem statements we are giving you. Simply add your
solutions by editing this latex document. To make it easier for the TAs to find
your solutions, please use the soln environment we provided as follows:
\begin{soln}
My solution is here.
\end{soln}
Your solution will then appear in blue, and be easier to differentiate from the
questions.
2. If you need more space, add a page between the existing pages using the
\newpage command.
3. Export the completed assignment as a PDF file for upload to gradescope.
4. On Gradescope, upload only one copy per partnership. You must identify
you group via Gradescope, not doing so may result in loosing some marks
5. You must also tell us, via Gradescope, where each of the problem parts
appears on your submission. You MUST align the regions for every problem,
even if your assignment solution isn’t complete. We will not be able to mark
any problem we can’t find. After uploading the .pdf you will a screen, where
you can click each question on the left, and click the corresponding page(s) for
which the question appears in. Because of this matching process, please allocate
at least 5 minutes prior to the deadline for submission. You must match your
answers with each question, not doing so may result in loosing some marks.
Academic Conduct: I certify that my assignment follows the academic
conduct rules for of CPSC 121 as outlined on the course website. As part of
those rules, when collaborating with anyone outside my group, (1) I and my
collaborators took no record but names away, and (2) after a suitable break,
my group created the assignment I am submitting without help from anyone
other than the course staff.
1
, CPSC 121 2021S2
1. [6 marks] Given the following definitions:
• S: the domain of all CPSC 121 students.
• G: the domain of all graded CPSC 121 activities.
• A(x, y): student x earns an “A” grade on activity y
• B(x): student x receives a colourful balloon (from the CPSC 121 teaching team).
Now consider the predicate logic statements:
Statement 01: ∀x ∈ S, ∀g ∈ G, A(x, g) ↔ B(x)
Statement 02: ∀x ∈ S, (∀g ∈ G, A(x, g)) ↔ B(x)
Statement 03: ∀x ∈ S, (∀g ∈ G, (∀y ∈ S, A(y, g))) ↔ B(x)
Describe how these statements differ, in terms of who receives a balloon and under what
conditions.
For statement 01, any number of students can receive balloons, and balloons are earned
per activity.
For statement 02, any number of students can receive balloons, but only one balloon can
be awarded when the student aces the entire course.
For statement 03, either nobody gets a balloon, or everybody gets a balloon. The balloons
are awarded if everyone in the class aces the entire course together.
2
