Discrete Mathematics Answers

Construct a truth table for each of these compound propositions

(p ⊕ q) → (¬q ↔ r)

How many different strings can be made from the letters in the word rat?

A boy lives at X and wants to go to school at Z. From his home to X he has to first reach Y

and then Y to Z. He may go X to Y by either 3 bus routes or 2 train routes. From there, he can

either choose 4 bus routes or 5 train routes to reach Z. How many ways are there to go from X to

Z?

Suppose there are 19 Math majors, 17 English majors, and no double majors. How many ways

are there to choose someone who is either a Math major or a English major?

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?