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C004Discrete Structures 1 FinalEXAM

Total questions: 100

Worksheet time: 2hrs 0mins

Name
Class
Date
1.

Translate this to english.


∀x(∀y love (x,y)→ (love(x,x))


Universe of discourse for the variable x is anyone and y is everyone.

love(x,y): Anyone loves everyone

love(x,x): Anyone loves himself

a)

Anyone who loves anyone, loves himself

b)

Anyone who loves everyone, loves himself

c)

Everyone who loves anyone, loves himself

d)

None of the above

2.

State wether the predicate logic is true or false.

Every new beginning comes from some other beginning end.


Predicate: ∀x∃yBeginning(x) ⇒ [Beginning(y) ∧ ComesFrom(x, end(y))]

a)

True

b)

False

3.

What is a proposition that is always false?

a)

Negation

b)

Tautology

c)

Contradiction

d)

Absolute

4.

p and q are both true propositions and r is a false proposition.


What is the truth value of ~r

a)

true

b)

false

c)

neither true nor false

d)

information is insufficient

5.

p and q are both true propositions and r is a false proposition.

What is the truth value of  q∧(∼r)q\wedge\left(\sim r\right)  ?

a)

true

b)

false

c)

neither true nor false

d)

information is insufficient

6.

p and q are both true propositions and r is a false proposition.

What is the truth value of  p∨(q∧(∼r))p\vee\left(q\wedge\left(\sim r\right)\right)  ?

a)

true

b)

false

c)

neither true nor false

d)

information is insufficient

7.

p and q are false and r is true.

What is the truth value of  ∼p\sim p  ?

a)

true 

b)

false

c)

neither true nor false

d)

information is insufficient

8.

p and q are false and r is true.

What is the truth value of  q↔rq\leftrightarrow r  ?

a)

true 

b)

false

c)

neither true nor false

d)

information is insufficient

9.

What is the first step in constructing a truth table?

a)

Perform the rules in propositional logic.

b)

Construct the negation of the compound statement.

c)

Form the table for assertion.

d)

Write the converse of the implication statement.

10.

If p is true and q is false, what is ~q→p?

a)

True

b)

False

11.

What is the truth value of the statement "Integers are rational numbers and rational numbers are real."?

a)

True

b)

False

12.

What type of logic is this table showing:

a)

AND

b)

OR

c)

NOT

d)

NOR

13.

This symbol, ∧, means?

a)

and

b)

or

c)

not

d)

if, then

14.

This symbol, ∨, means?

a)

and

b)

or

c)

not

d)

if, then

15.

This symbol,→ , means?

a)

and

b)

or

c)

not

d)

if, then

16.

What type of logic is this table showing:

a)

AND

b)

OR

c)

IF, THEN

17.

If Brent works this summer, he will have extra money. If Brent has extra money, then he can go on vacation. Therefore if Brent works this summer, he can go on vacation.


Which of the following is a premise in the argument above?

a)

If Brent works this summer, he will have extra money

b)

Therefore, if Brent works this summer, he can go on vacation

c)

Brent works this summer

d)

Brent can go on vacation

18.

If Brent works this summer, he will have extra money. If Brent has extra money, then he can go on vacation. Therefore if Brent works this summer, he can go on vacation.


Which of the following is the conclusion of the argument above?

a)

If Brent works this summer, he will have extra money

b)

Therefore, if Brent works this summer, he can go on vacation

c)

Brent works this summer

d)

Brent can go on vacation

19.

What type of logic is this table showing:

a)

AND

b)

OR

c)

NOT

d)

NOR

20.

What type of logic is this table showing:

a)

AND

b)

OR

c)

NOR

d)

XOR

21.

What type of logic is this table showing:

a)

AND

b)

OR

c)

NOT

d)

XOR

22.

Use the logic condition to find the value of X:


A and not B

a)

True

b)

False

23.

Use the logic condition to find the value of X:


Not A or B

a)

True

b)

False

24.

Use the logic condition to find the value of Y:


A or B or C

a)

True

b)

False

25.

Use the logic condition to find the value of X:


A or (B and C)

a)

True

b)

False

26.

Use the logic condition to find the value of W:


not A or B or C

a)

True

b)

False

27.

Use the logic condition to find the value of X:


A && (B || C)

a)

True

b)

False

28.

Which of the following ABC inputs results in a true statement for:

(A && !B) || C

a)

TTF

b)

FFT

c)

TFT

d)

FTF

e)

TFF

29.

Let p represent: Brent works this summer.

Let q represent: Brent takes a vacation.

What is the symbolic representation of this statement?

Therefore, Brent does not work this summer.

a)

∴~p

b)

∴~q

c)

~p

d)

~q

30.

Which of the following set of values would correctly complete this table?

a)

T F F F

b)

T T F F

c)

T T T F

d)

F T F T

31.

This symbol, → , means?

a)

AND

b)

NOT

c)

IF/ THEN

d)

IF AND ONLY IF

32.

"The burglar alarm will go off if either the door or the window or both are opened". This is an example of which type of Logic?

a)

AND

b)

OR

c)

NOT

d)

NOR

33.

Use the logic condition to find the value of X:


A Λ (B || C)

a)

True

b)

False

34.

Use the logic condition to find the value of W:


A & ~(B | C)

a)

True

b)

False

35.

"I like pancakes with either Jam or cream cheese but not both!"

This is an example of which type of logic?

a)

AND

b)

OR

c)

XOR

d)

NOR

36.

What is the result of the following condition?


3 * 2 == "six"

a)

True

b)

False

37.

What is the result of the following condition?


4 * 3 == 12 and 3 * 2 == 7

a)

True

b)

False

38.

What is the result of the following condition?


"Jack" == "Jack" and "Mike" == "Mike" or 3 * 2 ==7

a)

True

b)

False

39.

What is the output of the following condition?


name = "Ali"

name == "Ali" or name == "Bob"

a)

True

b)

False

40.

What is the output of the following condition?


number = 120

number > 100 and number < 150

a)

True

b)

False

41.

What is the output of the following condition?


number = 150

number != 0 and number < 100

a)

True

b)

False

42.

Which phrase that not indicates UNIVERSAL QUANTIFIER?

a)

For all

b)

For every

c)

For each

d)

For some

43.

Which phrase that not indicates EXISTENTIAL QUANTIFIER?

a)

There exist

b)

There is a

c)

For each

d)

For some

44.

"All" is a phrase that indicates

a)

Universal Quantifier

b)

Existential Quantifier

45.

Symbol for EXISTENTIAL QUANTIFIER

a)

∃

b)

∀

c)

v

d)

¬

46.

Symbol for UNIVERSAL QUANTIFIER

a)

∃

b)

∀

c)

v

d)

¬

47.

"Every" is a phrase that indicates

a)

Universal Quantifier

b)

Existential Quantifier

48.

"Some" is a phrase that indicates

a)

Universal Quantifier

b)

Existential Quantifier

49.

"There exists" is a phrase that indicates

a)

Universal Quantifier

b)

Existential Quantifier

50.

Let M(x) = x loves Mathematics,

where x consists of all students.


Translate ∀xM(x) into English sentence

a)

All students love Mathematics.

b)

Some students love Mathematics.

c)

There exists students love Mathematics.

d)

There is a student loves Mathematics.

51.

Let M(x) = x loves Mathematics,

where x consists of all students.


Translate ∃x¬M(x) into English sentence

a)

There is a student who is does not love Mathematics.

b)

There is a student who is loves Mathematics.

c)

All students does not love Mathematics.

d)

All students love Mathematics.

52.

This logic deals with analyzing formally valid reasoning based on their propositions.

a)

Class Logic

b)

Propositional Logic

c)

Quantificational Logic

d)

Modern Logic

53.

Class logic indicates the belonging or non-belonging of an element within a set, according to the properties it shares with it.

a)

TRUE

b)

FALSE

54.

Propositional Logic focuses on the relationship between a quantity and the propositions, distinguishing between individuals and their predicates.

a)

TRUE

b)

FALSE

55.

Use quantifiers that allude to the extension of the individuals to whom the predicate is attributed.

a)

Example of Class Logic

b)

Example of Quantificational Logic

c)

Example of Propositional Logic

d)

Symbolic Language

56.

if i choose number one what is the next to second one?

a)

3

b)

2

c)

1

d)

3.1

57.

What can be broken, but is never held?

a)

the word

b)

his choice

c)

is that you?

d)

a promise

58.

What is the name of your Instructor in Discrete Structure

(a)  

59.

Look at the Venn Diagram.

How many yellow lady bugs are there?

a)

There are 6 yellow lady bugs

b)

There are 11 yellow lady bugs

c)

There are 5 yellow lady bugs

60.

How many yellow and red lady bugs in total?

a)

11 lady bugs

b)

14 lady bugs

c)

17 lady bugs

61.

Look at the Venn Diagram.

How many children that only like to play yo yo?

a)

2 children

b)

3 children

c)

4 children

62.

How many children like to play both kite and yo yo?

a)

8 children

b)

3 children

c)

6 children

63.

Look at the Venn Diagram.

How many animals that only live on land?

a)

6 animals

b)

4 animals

c)

8 animals

64.

What animals that live both on the land and in the water?

a)

Fish, turtle, crocodile and frog

b)

Cow, fish, frog and turtle

c)

Crocodile and frog

65.

How many animals that only live in the water?

a)

4 animals

b)

6 animals

c)

8 animals

66.

Look at the Venn Diagram.

How many children that only like to read?

a)

3 children

b)

9 children

c)

8 children

67.

Who likes both reading and painting?

a)

Lusi and Ani

b)

Lusi

c)

Ani and Rafi

68.

How many children are altogether?

a)

11 children are altogether

b)

12 children are altogether

c)

13 children are altogether

69.
Ordered pair (0,0) is also known as the ___.
a)
y-axis
b)
x-axis
c)
origin
d)
I love Math!
70.
In an ordered pair the first number represents which axis?
a)
x
b)
y
c)
z
d)
w
71.
In the ordered pair (4,9), which number is the y-coordinate?
a)
4
b)
9
c)
neither
d)
both
72.
How do you write an ordered pair?
a)
(X,X)
b)
(Y,X)
c)
(X,Y)
d)
(Y,Y)
73.
In which quadrant is the following point found?
(-3, -12)
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV
74.
If you were to plot the point (4, -12) what would be the correct method?
a)
Up 4, left 12
b)
Right 4, up 12
c)
Down 4, left 12
d)
Right 4, down 12
75.
What is the vertical number line in the coordinate plane called? 
a)
y-axis
b)
origin
c)
quadrant
d)
x-axis
76.

Which of the following element/member does not belong to the given collection?
{goat, carabao, deer, dog, cow}

a)

goat

b)

carabao

c)

deer

d)

dog

e)

cow

77.

Which of the following element/member does not belong to the given collection?
{6, 8, 9, 10, 12}

a)

6

b)

8

c)

9

d)

10

e)

12

78.

Which of the following element/member does not belong to the given collection?
{Albay, Catanduanes, Ilocos Sur, Camarines Norte, Sorsogon}

a)

Ilocos Sur

b)

Camarines Norte

c)

Catanduanes

d)

Albay

e)

Sorsogon

79.

Which of the following element/member does not belong to the given collection?
{orange, yellow, red, blue}

a)

blue

b)

red

c)

yellow

d)

Orange

80.

"Well-defined" means that a given object can be categorically identified to belong to the (a)   or not.

81.

It is the set containing all the elements of which all other sets are subsets.

a)

Subset

b)

Proper subset

c)

Universal set

d)

Null set

82.

A set that every elements can be found in another set.

a)

Subset

b)

Proper subset

c)

Universal set

d)

Null set

83.
The image represents which of the following?
a)
intersection, "and"
b)
union, "or"
c)
intersection, "or"
d)
union, "and"
84.
The image represents which of the following?
a)
intersection, "and"
b)
intersection, "or"
c)
union, "and"
d)
union, "or"
85.

P(Soda) =

a)

200/400

b)

158/400

c)

50/200

d)

120/200

86.
P(Pizza ∪ Water) =
a)
182/400 + 140/400 - 58/400
b)
182/400 + 140/400 - 0
c)
58/400 + 140/400 -182/400
d)
182 + 140 - 58
87.
What statement does the shaded region represent?
a)
A or B
b)
A and B
c)
A
d)
B
88.
What is P(not sport)?
a)
24/50
b)
26/50
c)
3/50
d)
23/50
89.
What statement does the shaded region represent?
a)
A or B
b)
Not A
c)
A and B
d)
Not B
90.
Which of the following statements are true for the Venn diagram shown?
a)
A ∩ B = ⊘
b)
A ⋃ B = ⊘
c)
A ⋃ B = A
d)
A ⋂ B = A
91.

Let C={2, 5, 7, 10} and B={2, 4, 6, 8}. Find C U B

a)

{2,4,6,8,10}

b)

{2,4,5,6,7,8,10}

c)

{2, 4, 5, 6, 7, 8, 10}

92.

The Cardinality is the number of elements in a set.

a)

true

b)

false

93.

A set of stars in the sky

a)

a. Millions

b)

b. Billions

c)

c. Finite

d)

d. Infinite

94.

B = {-3, -1, 1, 3, 5, 7}

a)

a. 2

b)

b. 4

c)

c. 6

d)

d. 8

95.

B = {-3, -1, 1, 3, 5, 7}

a)

a. 2

b)

b. 4

c)

c. 6

d)

d. 8

96.

A = {A, B, C, D, E, F, G, H}

a)

a. 2

b)

b. 4

c)

c. 6

d)

d. 8

97.

A set of vans laptop

a)

a. 2

b)

b. 4

c)

c. 6

d)

d. 0

98.

A set of stars in the Philippine Flag

a)

a. Null Set or Empty Set

b)

b. Billions

c)

c. Finite

d)

d. Infinite

99.

A set of stars in the Philippine Flag

a)

a. Null Set or Empty Set

b)

b. 6

c)

c. 3

d)

d. 9

100.

A set of colors of the Philippine Flag

a)

a. 2

b)

b. 3

c)

c. 4

d)

d. 5

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