Discrete Mathematics Answers

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 =

A. Let p and q be propositions

p: 4 is a rational number

q: 3 is an irrational number.

Express each of these propositions as an English sentence:

1. ¬p =

2. p v q =

3. p ^ q =

4. p→q =

5. p ↔q =

• Let P(x, y) be the statement “student x has taken class y”, where the domain for x consists of all students and y consists of all computer engineering courses at your school.

• Express each of the quantification in English sentences

1. ∀x ∀y P(x,y)

2. ∀x Ǝy P(x,y)

3. Ǝx ∀y P(x,y)

4. Ǝx Ǝy P(x,y)