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.