MAT 123A

Hand-in Assignment #1

Due Thursday, October 2 (at the beginning of class)

NO LATE ASSIGNMENTS ACCEPTED

(If you know you will miss class, it is your responsibility to get your assignment into my mailbox in SB 308 before class)

 

I will hand out solutions after I collect the assignments, so I recommend that you keep a copy of the assignment for your notes.

 

Please work independently on the following problems.  You are not permitted to obtain help from friends or tutors for this assignment.  Write up your solutions neatly on separate paper and justify all answers.  If you have multiple pages they must be stapled together (not paper clipped!) to receive full credit.

 

1)                  Shade in a Venn diagram to represent each of the following sets:            

 

a.       (B È C) – A

b.     

c.      

 

2)                  Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is a universal set, and let E = {1, 3}, F = {1,4, 5} and G = {2, 3, 7, 8}.  List the elements of the following sets:

 

a.                   F ´ E

 

b.                  F Ç G

 

c.                   F – G

 

d.                 

 

3)                  In a class of 25 students, suppose 12 are seeing a math tutor and of those, 8 are also seeing an English tutor.  An additional 10 students are seeing an English tutor only.  The rest aren’t seeing any tutors.

a.       How many students are seeing at least one tutor?

b.      How many students in the class are not seeing a tutor?

c.       How many are seeing a math tutor but not an English tutor?

Be sure to justify your answers.

 

4)         a.         Explain what it means for two sets to have a one-to-one correspondence.

b.                  Is it possible for the sets A = {2, 4, 7} and B = {1, 2, 4, 7} to have a one-to-one correspondence?  If so, describe one.  If not, explain why not.

c.                   Is it possible for the sets C = {1, 2, 3, 4, 5, . . . } and E = {2, 4, 6, 8, 10, . . .} to have a one-to-one correspondence?  If so, describe one.  If not, explain why not.

 

5)      Let M = the set of all students in one section of MAT 123.  There are 17 elements in set M.  How many subsets does M have?  How many proper subsets?  Justify your answers. (Obviously you can’t list all the subsets.  You might want to use a calculator to figure out your final answer.) (hint: see problem #35 on p. 55)

 

 

6)            Convert to Roman numerals:   a.         1987                b.         2551                c.         764

 

 

7)            Convert to numbers we use:    a.         MMMCMXXIV           b.         MDCCXLII