#### Question Details

Answered: - I'm completely lost on this, i finished #1. It is due tonight, im

I'm completely lost on this, i finished #1. It is due tonight, im panicking. HELP !

Midterm (Show/Explain all Work)

IST 230

Chapter 1

1.

Complete the following truth table for

( p ? ( ?r )) ? q .

(4 points)

p

q

r

?r

p? ( ?r )

( p ? ( ?r )) ? q

T

T

T

T

F

F

F

F

T

T

F

F

T

T

F

F

T

F

T

F

T

F

T

F

F

T

F

T

F

T

F

T

F

T

F

T

F

F

F

F

T

T

F

F

T

T

T

F

Chapter 2

2. In this question, the domain of discourse is the set of people in our IST 230 class. Define the following

predicates:

T(x): x is more than six feet tall.

S(x): x is less than five feet tall.

Translate the following English statements into a logical expression with the same meaning.

a.

The negation of ?Everyone in our IST 230 class is more than six feet tall.? Translate in two ways:

one using a universal quantifier and one using an existential quantifier. (4 points)

b. ?No one in our class is less than five feet tall.? (2 points)

3.

Let A and B be defined as follows:

A = {Tom, Bo}

B = {Java, Python, R}

a. Write the cross product AxB as a set of ordered pairs. (4 points)

b. Write the cross product BxA as a set of ordered pairs. (4 points)

Midterm (Show/Explain all Work)

IST 230

c. Write one ordered pair that is in the set AxB but is not in the set BxA. (2 points)

Chapter 3

4.

Let sets A and B be defined as follows:

A = {Java, Python, R}

B = {Tom, Bo}

a. List as a set of ordered pairs one 1-1 function from A to B, or explain why no such function exists.

(5 points)

b.

List as a set of ordered pairs one onto function from A to B, or explain why no such function

exists. (5 points)

c.

Let f:B ? A be given by this set of ordered pairs:

f = { (Tom, Java), (Bo, Python) }

If f has an inverse function, call it g and list g as a set of ordered pairs. If f has no inverse function,

explain why not. (5 points)

5.

Let A = {a1, a2} and B = {b1, b2, b3}. Let the function f:A ? B be given by the following set of ordered

pairs: f = {(a1,b2),(a2,b3)}. (10 points)

List as a set of ordered pairs a function g with the property that for all a in A g(f(a)) = a, and show that this

property holds. HINT: First identify the domain and the target of the function g. Second, think of g as

?undoing? what f does.

Chapter 4

Midterm (Show/Explain all Work)

6.

IST 230

Given the following circuit, complete the output column on the table below. (5 points)

x

1

1

1

1

0

0

0

0

Inputs

y

1

1

0

0

1

1

0

0

Output

z

1

0

1

0

1

0

1

0

Chapter 5

7. Draw the arrow diagram and the matrix representation for the following relation on the set {1, 2, 3, 4}.

R = { (1, 1), (1,4), (2,2), (3,4), (3, 2), (2, 1), (1, 3), (4,2)}.

a.

Draw the arrow diagram for R (a scan of a hand-drawn image is OK). (5 points)

Midterm (Show/Explain all Work)

IST 230

b. Draw the matrix representation for R. (5 points)

c.

8.

Explain why the relation R is or is not reflexive. (5 points)

You answer must begin with either ?The relation R is reflexive, because? or ?The relation R is not

reflexive, because?.

Define the following two relations on the set {a, b, c, d} (10 points)

S = { (a, b), (a, c), (c, d), (c, a) }

R = { (b, c), (c, b), (a, d), (d, b) }

Write S ? R as a set of one or more ordered pairs.

Chapter 6

9.

Write an algorithm in pseudo-code with the following input and output (10 points).

Input: a1, a2,..., an, a sequence of integers.

Output: The smallest integer in the sequence.

10. What is the value of count after the last iteration of the outer for loop? Be sure show your work. (10

points)

count :=0

IST 230

Midterm (Show/Explain all Work)

For i= 1 to 2

For j=1 to 2

count :=j(count + 2i)

End-for

End-for

Chapter 7

11. Find the next three terms (terms

a2

Here, the right-hand side is j times the quantity (count + 2i)

a3

a 4 ) of the recursively defined sequence

a k =ak ?1 +3 k , for all integers k ? 2 , where a1=1 . (5 points)

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