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Specification for Assignment 2 for COMP1805 (Fall 2016)

Specification for Assignment 2 for COMP1805 (Fall 2016)

General Instructions This is your second assignment for the semester. Your answers must either be neatly

handwritten (using either blue or black) and then scanned or digitally photographed,

or created electronically (using Microsoft Word or Google Docs, for instance) and

saved as one or more "pdf" documents. If your submission for this assignment includes multiple files then these files must be

compressed into a single "zip" file, and you will submit this file using cuLearn. If your

submission is a single "pdf" document, you need not compress it into a "zip" file. The compressed archive (i.e., the "zip" file) must be named "a2.zip". Any handwritten pages must be "jpeg" files named "a2-file-x-of-y.jpg" Any electronically created files must be "pdf" files named "a2-file-x-of-y.pdf" The due date for this assignment is October 19, 2016, by 11:30pm. Since assignment solutions are released promptly after the due date, late

assignments will never be accepted under any circumstances. This includes, but is

not limited to, medical or technical issues. Once you have uploaded your submission, you are expected to download your own

submission and review the file to ensure that you have submitted the correct files and

that none of the files have been corrupted or are otherwise unreadable. If your submission for this assignment is unsatisfactory (e.g., corrupted files,

unreadable handwriting, etc.) you will not be given an opportunity to resubmit. If you

have any doubts about the legibility of your submission, you must contact the

instructor at least 48 hours before the assignment deadline. You are strongly advised to attempt to submit your assignment (or at least the part

that you have already completed) at least two hours before the deadline. Specification for Assignment 2 for COMP1805 (Fall 2016)

Assignment Questions 1. Determine whether or not the following arguments are valid. If they are valid, then

state the rules of inference used to prove validity. If they are invalid, outline

precisely why they are invalid.

a. If I have parents who are martians then I must live on Mars. I live on Mars.

Therefore I must have parents who are martians.

b. If I can drive a car or ride a bicycle, then I can commute to work. Anyone that

rides a bicycle does not have a parking space. I don't have a parking space.

Therefore I must ride a bicycle.

c. Everyone who has a PC plays computer games. Everyone student taking

COMP1501 next semester plays computer games. Therefore every student

taking COMP1501 next semester has a PC.

d. All fish swim. All animals that swim can breathe water. I am an animal and I

can swim. Therefore I must be a fish.

2. The floor of a real number x, denoted ??, is the unique integer that satisfies the

expression ?? ? < ?? + 1.

a. Compute ?1.25?, ?1.75?, ??0.25?, ??0.3? + ?0.3? + ?0.3? + 2?

b. Prove or disprove that ?? + ?? ? ? + ? ? 1.

3. What is the power set of {2, 4, 8} ?

4. Prove that ?4 + ?3 + ?2 is an irrational number.

5. Prove that 8 + 4

?3 is an irrational number. 6. List explicitly the members of the following sets.

a. { | 0 ? < 20 ? ? ? ? ?? }

b. { | ? ? 10 }

c. { | ? 1805 ? ? ? } Specification for Assignment 2 for COMP1805 (Fall 2016)

Assignment Questions 7. Let = {2, 4, {2,4}, {6}, {2, 4, 6}} and

answer the following questions. T= {{4, 6, 8, 10, 12, 14, 16, 18}, {4}, 2} and a. Which set has the larger cardinality?

b. What is the intersection ? ?

c. What is the cardinality of the union ? ?

8. Determine whether or not the following are valid. Justify your answer by using

either set identities or membership tables.

a. ( ? ) ? ( ? ) = ( ? ? ) ? ( ? ) ? ( ? )

b. ( ? ? ) ? ? ( ? ) = ( ? ) ? ( ? )

9. Draw the Venn Diagrams for the following sets.

a. ( ? ) ? ( ? ) = ( ? ? ) ? ( ? ) ? ( ? )

b. ( ? ? ) ? ? ( ? ) = ( ? ) ? ( ? )

10. What is the intersection, A, of the set of all the digits that appear in your student

number, B, and the set of all even numbers, C. Draw the Venn Diagram for sets A, B,

and C.

11. What is the intersection, X, of the set of all the characters that appear in your last

name, Y, and the set of all characters that appear in the set of hexadecimal digits, Z.

Draw the Venn Diagram for sets X, Y, and Z.

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