Discrete Mathematics Answers

Provide the answers to the following items. (5 items x 3 points)

1.      Given A = {2, 4, 6, 8} and B = {3, 4, 5, 6}, determine:

a)      A U B

b)     A ∩ B

2.      Given A = {3, 5, 7, 9} and B = {4, 5, 6, 7}, determine:

a)      A - B

b)     B - A

c)      A ∩ B

Find f ◦ g and g ◦ f , where f (x) = 3x - 2 and g(x) = 2x + 2, are functions from R to R

"\\forall" x,y "\\in" R, x² +y²=9

Write in the form “if p then q”, then write the converse, inverse and contra positive of each of the following implications.

1. It is necessary to do your homework to get the passing grade.

a.  Converse (q →p) =

b. Contra positive (q→¬p )=

c.  Inverse (p→¬q ) =  

2. You can access the school Wifi only if you are enrolled.

a.  Converse (q →p) =

b.  Contra positive (q→¬p )=

c.  Inverse (p→¬q ) =   

3.   Mark gets a high grade whenever he studies his lesson.

a. Converse (q →p) =

b. Contra positive (q→¬p )=

c. Inverse (p→¬q ) =

4.  If you read your lessons everyday, you will pass all your course.

a.  Converse (q →p) =

b.  Contra positive (q→¬p )=

c.  Inverse (p→¬q ) =

5.  If it rains today, I will stay home and read my lessons.

d. Converse (q →p) =

e. Contra positive (q→¬p )=

f. Inverse (p→¬q ) =

how many different elements does A x B have if A has m elements and B has n elements?

If A = {5,6,7} and B = {2,3}, {(2,6),(2,5),(3,7)} ⊆ B×A.

Find A x B if A={0,1,3} and B={1,2,a,b}.

B.  Let p and q be propositions

p: You make a correct program

q: You get an A

Write each of the following sentences in terms of p, q and logical connectives:

______________1. You do not make a correct program.

______________2. You make a correct program, but you do not get an A.

______________3. Making a correct program is sufficient for getting an A.

______________4. You get an A but you do not make a correct program.

______________5. Whenever you get an A, you are making a correct program.

A.         Let p and q be propositions

p: 4 is an even integer

q: 5 is an odd integer

Write each of the following sentences in terms of p, q and logical connectives:

______________1. 4 is an even integer and 5 is an odd integer.

______________2. 4 is not an even integer or 5 is an odd integer.

______________3. If 4 is an even integer then 5 is an odd integer.

______________4. 4 is an even integer whenever 5 is an odd integer.

______________5. 4 is not an even integer if an only if 5 is not an odd integer.

B. Let p and q be propositions.

p: Cristina is a computer science major.

q: Leonardo is an Information Technology major.

Express each of these proposition as an English sentence:

1. q =

2. pq =

3. pq =

4. ¬q V (¬p ^ q )=

5. p ↔q =