Assignment No. 2 EECS 210 Discrete Structures

Assignment No. 2
EECS 210
Discrete Structures

Submit deliverables in a single zip file to Canvas
Name of the zip file: FirstnameLastname_Assignment2 (with your first and last name)
Name of the Assignment folder within the zip file: FirstnameLastname_Assignment2
Deliverables:
1. Copy of Rubric2.docx with your name and ID filled out (do not submit a PDF)
2. Source code.
3. Screen print showing the successful execution of your code or copy and paste the
output from a console screen to a Word document and PDF it.
Assignment:
• You may use any language you want, but if you want help from me or one of the
SIs, you should probably use C++ or Python.
• Create a program for the following:
1. Prove (true) or disprove (false) the following assertions for the domain of
{0,1,2,3,4,5,6,7,8,9,10}. For the universal quantifier, show at least one of the
numbers in the domain that disproves the assertion. For the existential
quantifier, show at least one number in the domain that proves the assertion:
a) ∃x P(x), where P(x) is the statement “x<2”
b) ∀x P(x), where P(x) is the statement “x<2”
c) ∃x (P(x) ∨ Q(x)) where P(x) is the statement “x<2” and where Q(x) is
the statement “x>7”
d) ∀x (P(x) ∨ Q(x)) where P(x) is the statement “x<2” and where Q(x) is
the statement “x>7”
e) Prove De Morgan’s Law for the Existential Quantifier where P(x) is
the statement “x<5”
f) Prove De Morgan’s Law for the Universal Quantifier where P(x) is the
statement “x<5”
2. Find the following truth values for the domain of {0,1,2,3,4,5,6,7,8,9,10}
where P(x,y): x ∙ y = 0. Show the values in the domain that either make the
assertions true or false. (See Example 1 and 2 for “Order of Quantifiers” in the
9-1 lecture on Nested Quantifiers).
a) ∀x∀yP(x,y)
b) ∀x∃yP(x,y)
c) ∃x∀yP(x,y)
d) ∃x∃yP(x,y)
• Print out a line between each of the above indicating which number your program
is answering, (e.g., 1b).
• Provide comments that explain what each line of code is doing. See rubric below.
Rubric for Program Comments
Exceeds Expectations
(90-100%)
Meets Expectations
(80-89%)
Unsatisfactory
(0-79%)
Software is adequately
commented with prologue
comments, comments
summarizing major blocks of
code, and comments on every
line.
Prologue comments are present
but missing some items or some
major blocks of code are not
commented or there are
inadequate comments on each
line.
Prologue comments are missing
all together or there are no
comments on major blocks of
code or there are very few
comments on each line.
Remember:
• Your Programming Assignments are individual-effort.
• You can brainstorm with other students and help them work through problems in
their programs, but everyone should have their own unique assignment programs.