CS101-1

Question 1

Given the following statements:

Statement A: When 4x+2 = 0, x is 0.5.

Statement B: 20 is a prime number.

Statement C: A and B are true.

Identify the truth value of Statement C.

Answer 1

False

Question 2

Statement A: 5 + 23 is 28.

Statement B: 31 - 2 is 33.

Statement C: A or B is not true.

Identify the truth value of Statement C.

Answer 2

False

Question 3

Evaluate: True AND False

Answer 3

False

Question 4

Evaluate: NOT False AND NOT False

Answer 4

True

Question 5

If p is true and q is false, what is the truth value of the expression p → q?

Answer 5

False

Question 6

Which of the following is an example of a compound proposition?

Show answer choices

q

not p

p and q

p

Answer 6

p and q

Question 7

What is a compound Proposition?

Answer 7

statement that combines 2 or more propositions using connectives (and, or, but)

Question 8

What does the logical operator ‘¬’ represent?

Show answer choices

Conjunction

Disjunction

Implication

Negation

Answer 8

Negation

Question 9

What is the definition of a proposition in logic?

Show answer choices

A statement that is either true or false.

A sentence that can be either a statement or a question.

A command or question.

An assumption that is not verified.

Answer 9

A statement that is either true or false.

Question 10

Which of the following is NOT a logical constant?

Show answer choices

X

1

True

False

Answer 10

X

Question 11

What is a logical constant

Answer 11

a symbol that has the same meaning no matter what

Question 12

hat does proof by exhaustive checking involve?

Show answer choices

Using a single example to prove the statement is true.

Assuming the proposition is true and finding a counterexample.

A method of proof that is never conclusive.

Checking all possible cases to see if the proposition holds true.

Answer 12

Checking all possible cases to see if the proposition holds true.

Question 13

What is the truth table used for?

Show answer choices

To define the syntax of logical expressions.

To simplify complex propositions.

To determine the truth values of propositions under different scenarios.

To create logical conclusions.

Answer 13

To determine the truth values of propositions under different scenarios.

Question 14

In propositional logic, what does the symbol ‘→’ signify?

Show answer choices

Conjunction, meaning ‘and’.

Negation, meaning ‘not’.

Disjunction, meaning ‘or’.

Implication, meaning ‘if… then…’

Answer 14

Implication, meaning ‘if… then…’

Question 15

In conditional proof, what must be demonstrated?

Show answer choices

A counterexample to the premise.

That if the premise is true, then the conclusion must also be true.

That both the premise and conclusion are true.

That the conclusion can be true regardless of the premise.

Answer 15

That if the premise is true, then the conclusion must also be true.

Question 16

When constructing a proof by contradiction, what must you assume initially?

Show answer choices

That all premises are valid.

That no conclusions can be drawn.

That the proposition is true.

That the proposition you want to prove is false.

Answer 16

That the proposition you want to prove is false.

Question 17

Which of the following statements best defines ‘if and only if’ (↔)?

Show answer choices

It is a condition that relies solely on the first statement.

Either one can be true for the statement to hold.

Both sides must have the same truth value.

The first must be true for the second to be true, but not vice versa.

Answer 17

Both sides must have the same truth value.

Question 18

Which of the following is NOT a valid method of proof?

Show answer choices

Direct proof.

Proof by contradiction.

Proof by contradiction that involves guessing.

Constructive proof.

Answer 18

Proof by contradiction that involves guessing.

Question 19

In the expression p ∨ q, what does the ‘∨’ operator represent?

Show answer choices

Logical OR

Logical AND

Logical NOT

Logical implication

Answer 19

Logical OR

Question 20

Question 15
1
/
1
What does the conjunction operator ‘∧’ indicate?

Show answer choices

Both statements must be false.

At least one statement is true.

One statement implies the other.

Both statements must be true.

Answer 20

Both statements must be true.

Question 20

Which logical operator indicates that at least one of the statements is true?

Show answer choices

Logical AND (∧)

Logical OR (∨)

Implication (→)

Negation (¬)

Answer 20

Logical OR (∨)

Question 21

What do we call the situation where ‘p’ implies ‘q’ and ‘q’ implies ‘p’?

Show answer choices

A biconditional statement.

An implication.

A tautology.

A disjunction.

Answer 21

A biconditional statement.

Question 22

What is a minimal counterexample?

Show answer choices

An example that has multiple variables.

The simplest instance where the proposition fails to hold.

An example that supports the proposition.

The most complex example that invalidates the proposition.

Answer 22

The simplest instance where the proposition fails to hold.

Question 23

Which method would you use to prove a proposition that claims something is true for all integers?

Show answer choices

Using a single counterexample.

Mathematical induction.

Direct computation of values.

Exhaustive checking of all integers up to a specified number.

Answer 23

Mathematical induction.

Question 24

Let A = {34, 67, 21, 94, 43};

Let B = {22, 21, 14, 19, 67};

Let C = {94, 67, 34, 32, 22};

And A∈U, B∈U C∈U.

Which of the following elements belong to B’\C? Select all that apply. Partial points are awarded.

Show answer choices

94

67

43

21

32

Answer 24

43

Question 25

Question 3
5
/
5
Let A = {34, 67, 21, 94, 22};

Let B = {22, 42, 14, 19, 67};

Let C = {92, 21, 34, 32, 22};

And A∈U, B∈U C∈U.

Which of the following elements belong to (C’∪B)? Select all that apply. Partial points are awarded.

Show answer choices

21

67

92

34

22

Answer 25

67

Question 26

Question 4
5
/
5
Let A = {34, 67, 21, 94, 22};

Let B = {22, 75, 14, 86, 67};

Let C = {32, 79, 94, 75, 22};

And A∈U, B∈U C∈U.

Which of the following elements belong to (A∩C)’? Select all that apply. Partial points are awarded.

Show answer choices

67

34

94

75

22

Answer 26

67

34
75

Question 27

Question 5
5
/
5
Let A = {34, 67, 21, 94, 43};

Let B = {22, 21, 14, 19, 67};

Let C = {94, 67, 34, 32, 22};

And A∈U, B∈U C∈U.

Which of the following elements belong to AΔC? Select all that apply. Partial points are awarded.

Show answer choices

21

64

32

43

22

Answer 27

21

32

43

22

Question 28

Question 1
0
/
5
Which of the following is considered a set? Select all that apply. Partial points will not be provided.

Show answer choices

J = {all natural even numbers that are less than 25 but greater than 26}

G = {apple, banana, orange, melon, banana}

Y = { x^2 | x ∈ N }

A = {5, 2, 8768, 1}

O = {1, 2, 3, 5, 8, 13, …}

Answer 28

J = {all natural even numbers that are less than 25 but greater than 26}

Y = { x^2 | x ∈ N }

A = {5, 2, 8768, 1}

O = {1, 2, 3, 5, 8, 13, …}

Question 29

Consider this set statement:

A space equals space left curly bracket space 12 space comma space 5 space comma space 3 space comma space minus 2 space right curly bracket
B space equals space left curly bracket space x plus 2 space vertical line space space x element of A space right curly bracket
C space equals space left curly bracket space y minus 7 space vertical line space space y element of B space right curly bracket

Which of the following is a member of C? Select ALL that apply. Partial points are NOT awarded.

Hide answer choices

0

5

7

-9

1

Answer 29

0
7

Question 30

Consider this set statement:

F equals left curly bracket space a l l space s t r i n g s space t h a t space e n d space w i t h space apostrophe e apostrophe space right curly bracket
U equals left curly bracket a l l space s t r i n g s right curly bracket

Which of the following elements is a member of F’? Select ALL that apply. Partial points are NOT provided.

Hide answer choices

eeeeeeeeeeeeeeeeeeeeeee

equipment

;seotu;wjrecrunse;uc;fuodfjodsslkfe’

mahiwagang salamin kailan ba nya aaminin kanyang tunay na pagtingin

adorable

Answer 30

equipment

;seotu;wjrecrunse;uc;fuodfjodsslkfe’

mahiwagang salamin kailan ba nya aaminin kanyang tunay na pagtingin

Question 31

Consider this set statement:

D equals left curly bracket space x plus 1 space vertical line space x element of natural numbers semicolon space x vertical ellipsis 2 right curly bracket

Which of the following is a member of the said set? Select ALL that apply. Partial points are awarded.

Partial and negative credit
Points may have been deducted for incorrect answers.
Hide answer choices

-1126298745

2937234983243

29374983572758

0

2047834791

Answer 31

2937234983243
2047834791

Question 32

Consider the following set statement:

H space equals space left curly bracket 1 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 comma space 17 comma space 19 comma space 23 comma space… right curly bracket

Which of the following is an element of the given set? Select ALL that apply. Partial points are NOT awarded.

Hide answer choices

28

67

43

Answer 32

67
43

Question 33

Consider this set statement:

A space equals space left curly bracket space 12 space comma space 5 space comma space 3 space comma space minus 2 space right curly bracket
B space equals space left curly bracket space x plus 2 space vertical line space space x element of A space right curly bracket
C space equals space left curly bracket space y minus 7 space vertical line space space y element of B space right curly bracket

Which of the following is not a member of B∩C? Select ALL that apply. Partial points are NOT awarded.

Hide answer choices

-2

5

0

7

6

Answer 33

-2

5

6

Question 34

Question 6
3
/
5
Consider this set statement:

G space equals space left curly bracket space x plus y space vertical line space space x space less than space 5 semicolon space x element of straight integer numbers semicolon space y element of straight real numbers space right curly bracket

Which of the following is a member of the given set above? Select ALL that apply. Partial points are awarded.

Partial and negative credit
Points may have been deducted for incorrect answers.
Hide answer choices

-32

2.3

3124

3

0

Answer 34

-32

2.3

3124

3

0

Question 35

Assume the following statements:

A equals left curly bracket space 67 space comma space 18 space comma space 28 space comma space 21 space right curly bracket
B equals left curly bracket space 12 space comma space 9 space comma space 11 space comma space 18 space right curly bracket
C equals left curly bracket space 23 space comma space 28 space comma space 67 space comma space 1 space right curly bracket
U equals left curly bracket space e l e m e n t s space i n space A comma space B comma space a n d space C space right curly bracket

Which of the following are not a member of (A∪C)? Select ALL that apply. Partial points will be provided.

Hide answer choices

18

11

1

67

12

Answer 35

11
12

Question 36

Which of the following is the difference between Tuples and Lists?

Hide answer choices

Tuples can only access two things at a time while lists can access any element anytime.

Lists can construct over existing lists to create new lists while tuples cannot.

Tuples can have multiple sub-tuples inside it while lists have several bubbles that could be rendered as a set.

Lists can be represented in a computer while tuples are offered in a more practical and real-world scenario.

Answer 36

Lists can construct over existing lists to create new lists while tuples cannot.

Question 37

This is the singular elements that can be used to construct a string.

Hide answer choices

Alphabet

Lemma

Language

Lambda

Answer 37

Alphabet

Question 38

Which of the following statements about strings, languages, and alphabets are true? Select all that apply. Partial points are awarded.

Hide answer choices

A language is a set of strings.

Alphabets are a set of elements that can form a string.

Strings are a set of alphabets.

Answer 38

A language is a set of strings.

Alphabets are a set of elements that can form a string.

Question 39

This is the operation where two strings are placed next to each other to form a new string.

Hide answer choices

contempolation

contradiction

construction

concatenation

Answer 39

concatenation

Question 40

A space equals space less than g comma space w comma space e comma space n greater than
B space equals space less than s comma space t comma space a comma space c comma space e comma space y greater than

What is cons(head(A), head(B)) ?

Hide answer choices

<n, y>

<g, s>

<g, t>

<w, e, n, t, a, c, e, y>

Answer 40

<g, s>

Question 41

Which of the following is considered two equal tuples? Select all that apply. Partial points are awarded.

Hide answer choices

(t, o, o, t) = (o, t, t, o)

(m, e, o, w) = (m, e, o, w)

(a, b, c) = (a, b, c)

(R, O, O, M) = (R, 0, O, M)

Answer 41

(m, e, o, w) = (m, e, o, w)

(a, b, c) = (a, b, c)

Question 42

Empty lists do not have heads or tails.

T

True

FALSE

Answer 42

True

Question 43

Given the following alphabet:

B space equals space left curly bracket m comma space a comma space l comma space o comma space i right curly bracket

Which of the following is a string over B? Select all that apply. Partial points are awarded.

Hide answer choices

mailaoiiioiiiooiiioooiiioo

ilaoilaoilaoilaoilao

llaollaollao

lmailoamilaiamilailamialomailm

mmlamiliml1ailaoilamiloa

Answer 43

mailaoiiioiiiooiiioooiiioo

ilaoilaoilaoilaoilao

llaollaollao

lmailoamilaiamilailamialomailm

Question 44

Given the sets below, which of the following is a member of A x B? Select all that apply. Partial points are awarded.

A space equals space left curly bracket 4 comma space 2 comma space 0 right curly bracket
B space equals space left curly bracket 6 comma space 9 right curly bracket
A space cross times space B space equals space left curly bracket space left parenthesis a comma space b right parenthesis space vertical line space a element of A semicolon space b element of B right curly bracket

Hide answer choices

{4, 6}

(0, 6)

(4, 9)

(9, 0)

(6, 2)

Answer 44

(0, 6)

(4, 9)

Question 45

This is the singular elements that can be used to construct a string.

Lambda

Language

Lemma

Alphabet

Answer 45

Alphabet

Question 46

Consider the following lists:

A space equals space less than g comma space w comma space e comma space n greater than
B space equals space less than s comma space t comma space a comma space c comma space e comma space y greater than

What is cons(A,B) ?

<g, w, e, n, <s, t, a, c, e, y»

«g, w, e, n>, s, t, a, c, e, y>

<g, w, e, n, s, t, a, c, e, y>

«g, w, e, n>, <s, t, a, c, e, y»

Answer 46

«g, w, e, n>, s, t, a, c, e, y>

Question 47

Given the following alphabets:

A space equals space left curly bracket a comma space b comma space c comma space d comma space e comma space f right curly bracket
B space equals space left curly bracket g comma space r comma space e comma space a comma space t right curly bracket

And assume C is a string over A and D is a string over B.

Which of the following strings would be valid when C and D are concatenated as CD? Select all that apply. Partial points are not awarded.

Hide answer choices

decaftea

fadedtear

greatface

bead

Λ

Answer 47

decaftea

fadedtear

bead

Λ

Question 48

Given the following alphabet:

E space equals space left curly bracket m comma space e comma space o comma space w right curly bracket

Which of the following is a string over E? Select all apply. Partial points are not awarded.

Hide answer choices

meomeowmeowmewoemwneowenw

mewmewmewmew

meowmeowmeowmeow

pspspspspsps

emowemowemowemwoemwemweowem

Answer 48

mewmewmewmew

meowmeowmeowmeow

emowemowemowemwoemwemweowem