DISCRETE STRUCTURES MIDTERM EXAMINATION

If you will be counting the total numbers of students inside a classroom, what type of date will you be having?

Group of answer choices

Discrete data

Continuous data

Discrete data

(p ∨ q)∨r ≡ p ∨ (q ∨ r)

Group of answer choices

no answer

The argument has no sense.

The argument is invalid.

The argument is valid.

The argument is valid.

Which of the following are equivalent sets?

Group of answer choices

X = {x : x is a prime number less than 10} Y = {x : x ∈ N, x ≤ 4}

P = {q, s, m, n} Q = {6, 9, 12}

No Answer

A = {1, 2, 3} B = {4, 5}

X = {x : x is a prime number less than 10} Y = {x : x ∈ N, x ≤ 4}

Given: (p ^ q) --> q = T

identify the logical equivalences that will be used to prove the logical expression.

(i) De Morgan's Law

(ii) Implication Law

(iii) Identity Law

(iv) Associative

(v) Distributive Law

(vi) Domination

Group of answer choices

i,ii,iv,vi,vii

no answer

ii,i,iv,vii,vi

i,iii,v,vi,vii

no answer

Two sets A and B that have no common elements are called ___________.

Group of answer choices

power sets

empty sets

disjoint sets

universal sets

disjoint sets

Which of the following is the roster notation for the set of distinct letters in the word humility.

Group of answer choices

all of the above

{h, u, m, i, l, i, t, y

h, u, m, m, i, l, i, t, y

{h, u, m, i, l, t, y}

{h, u, m, i, l, t, y}

Which of the following is an example of a Continuous data.

Group of answer choices

Instruments in a shelf

The number of students in a class

The height of children.

The number of workers in a company.

The height of children.

Discrete Structures is a foundational material for Computer Science.

Group of answer choices

True

False

True

Discrete Structures develop Mathematical reasoning.

Group of answer choices

True

False

True

When one or more connectives are present in a statement, one of them is the dominant or major connective. The major connective is shown by using ________________.

Group of answer choices

curly braces

parentheses

question mark

none of the above

parentheses

Complete the truth table

p q p ↔ q

T T T

T F F

F T F

F F ?

Group of answer choices

F

T

T

What is the operator for NOT?

Group of answer choices

Negation

all of the above

Conjunction

Conditional

Negation

Is the given expression a proposition?

Are you sick?

Group of answer choices

no

Yes

no

F ∧ F is F

Group of answer choices

True

False

True

What is the operator for If, then?

Group of answer choices

all of the above

Conditional

Biconditional

Negation

Conditional

F ⊕ F is T

Group of answer choices

True

False

False

A compound proposition is a combination of one or more propositions. It is formed by using _______________.

Group of answer choices

parentheses

none of the above

propositions

logical connectives

logical connectives

9.8 newtons is an example of a Discrete Data.

Group of answer choices

True

False

Which of the following is an example of a Discrete Data?

Group of answer choices

number of tickets sold

water temperature

Wind speed

volts of electricity

number of tickets sold

It deals with the design and analysis of algorithms.

Group of answer choices

Computer Science

Discrete Structures

Algorithms

Programming

Computer Science

Dijkstra's Algorithm is a type of what algorithm?

Group of answer choices

route finding algorithm

scheduling algorithm

optimization algorithm

audio and video compression algorithm

route finding algorithm

Data that involves round, concrete numbers that are determined by counting.

Group of answer choices

Discrete data

Continuous data

Discrete data

Which of the following is an example of a Discrete Data?

Group of answer choices

Wind speed

volts of electricity

number of customers who bought different items

water temperature

number of customers who bought different items

Math is not important in Discrete Structures.

Group of answer choices

True

False

False

Which of the following is an example of a Discrete data.

Group of answer choices

The speed of cars

Time to wake up

Number of languages an individual speaks.

The weight of a truck

Number of languages an individual speaks.

What is the operator for OR?

Group of answer choices

Disjunction

Negation

all of the above

Conjunction

Discrete data can take any value in an interval.

Group of answer choices

True

False

False

Which among the following are propositions?

Group of answer choices

x + 4 = 7

4 + x = 7

4+ 4 = 7

none of the above

none of the above

What is the symbol for the logical connective BICONDITIONAL?

Group of answer choices

¬

↔

⊕

→

↔

What is the operator for iff?

Group of answer choices

Conjunction

Biconditional

all of the above

Conditional

Biconditional

⊕ is the logical symbol for negation.

Group of answer choices

True

False

False

What is the negation of p?

Group of answer choices

→ p

¬p

∧ p

none of the above

¬p

What is the operator for AND?

Group of answer choices

Negation

none of the above

Conjunction

Disjunction

Conjunction

T ⊕ F is F

Group of answer choices

True

False

False

T ↔ F is T

Group of answer choices

True

False

False

It is better to create your own algorithm.

Group of answer choices

True

False

It depends on the application

It depends on the application

Is the given expression a proposition?

Give me your money.

Group of answer choices

Yes

no

no

What is the operator for the symbol, ¬?

Group of answer choices

Conditional

all of the above

Conjunction

Negation

Negation

Data that involves complex numbers that are measured across a specific time interval.

Group of answer choices

Continuous data

Discrete data

Continuous data

Is the following statement a tautology? p --> ~p?

Group of answer choices

no

Yes

no

The logical connective OR is true if one or both of the propositions are true.

Group of answer choices

True

False

True

Is the following statement a tautology? [(pvq)^~p]-->q

Group of answer choices

Yes

no

Yes

What is the cardinality of an empty set?

Group of answer choices

none of the above

0

infinite

1

0

Is this a argument valid or invalid?

I will sing a song

I will dance

Therefore I will sing a song and I will dance

Group of answer choices

invalid

valid

valid

What are the truth values of the following statement?

~(por.gify)biconditional_transp.gif(~pand.gif~q)

Group of answer choices

F, F, F,F

F,T,F,T

T, T, T, T

none of the above

https://docs.google.com/document/d/1G_TWqKCRRbVlUZUe-C5I4skcVTFuQNE9qaCe4yfzoHw/edit?usp=sharing

What are the truth values of the following statement?

(p and.q)conditional.-q.

Group of answer choices

F,T,T,T

F,F,F,F

none of the above

T,T,T,T

F,T,T,T

Determine if (P \ifthen Q) \lor (Q \ifthen P)is a tautology, contradiction or a contingency.

Group of answer choices

Tautology

Contingency

Contradiction

Tautology

A compound proposition that is always ___________ is called a tautology.

Group of answer choices

True

False

True

Find the final column of the truth table for p ↔ ~q.

Group of answer choices

TTTT

FTTF

FFTT

FFFF

FTTF

Find the final column of the truth table for ~(q → p).

Group of answer choices

FTFF

TTFF

TFTF

FFFF

FTFF

Determine the truth value for the statement by making a truth table when p is false, q is true, and r is false.

q → (p ∧ r)

Group of answer choices

none of the above

False

True

True and False

True

p ↔ ~q is a tautology.

Group of answer choices

True

False

False

Find the final column of the truth table for (p ∧ q) → (p ∨ q).

Group of answer choices

FTFT

TFTF

TTTT

FFFF

TTTT

(p ∧ q) → (p ∨ q) is a tautology

Group of answer choices

True

False

True

By using Universal Bound Law, is

p ∧ c ≡ p

True?

Group of answer choices

Yes

no

no

Convert:

¬ (p ∨ q)

using De Morgan's Law.

Group of answer choices

p ∧ ¬ p ≡ F

none of the above

¬ p ∧ ¬ q

q ∧ p

¬ p ∧ ¬ q

ommutative Law states that (p ∧ q) is logically equivalent to _________.

Group of answer choices

none of the above

(p ∨ q)

(q ∧ p)

(q ∨ p)

(q ∧ p)

Complete the truth table.

p q p ⊕ q

T T ?

T F T

F T T

F F F

Group of answer choices

F

T

F

Choose the matching proposition

Group of answer choices

John doesn't love everyone

John does not love anyone

There is someone John doesn't love

John loves everyone

https://docs.google.com/document/d/1G_TWqKCRRbVlUZUe-C5I4skcVTFuQNE9qaCe4yfzoHw/edit?usp=sharing

Which of the following is not an example of Discrete data.

Group of answer choices

Number of languages an individual speaks.

The speed of cars

The number of home runs in a baseball game

The number of test questions you answered correctly.

The speed of cars

Discrete data is counted.

Group of answer choices

True

False

True

Continuous data can only have specific values.

Group of answer choices

True

False

False

It is a statement that is always true.

Group of answer choices

Contingency

Tautology

Contradiction

none of the above

Tautology

~(pconditional_transp.gifq) is a contingency.

Group of answer choices

True

False

True

Distribution Law states that [p ∧ (q ∨ r)] is logically equivalent to __________.

Group of answer choices

none of the above

[(p ∨ q) ∧ (p ∨ r)]

[(p ∧ q) ∨ (p ∧ r)]

[p ∨ (q ∧ r)]

[(p ∧ q) ∨ (p ∧ r)]

(aand.gifb)conditional.gifb is logically equivalent to the statement aconditional.gif(aor.gifb)

Group of answer choices

True

False

True

p ∧ q is logically equivalent to ________

Group of answer choices

(¬p → ¬q)

¬ (p → ¬q)

(¬p → q)

(p → ¬q)

¬ (p → ¬q)

pvq is a contradiction.

Group of answer choices

True

False

https://docs.google.com/document/d/1G_TWqKCRRbVlUZUe-C5I4skcVTFuQNE9qaCe4yfzoHw/edit?usp=sharing

p → ~q is contingency.

Group of answer choices

True

False

True

A compound proposition that is neither a tautology nor a contradiction is called a ___________

Group of answer choices

Inference

Condition

Equivalence

Contingency

Contingency

Is the given expression a proposition?

The elephant is pink.

Group of answer choices

Yes

no

Yes

s the given expression a proposition?

X=x+3

Group of answer choices

no

Yes

no

Is ~p->p a tautology?

Group of answer choices

Yes

no

no

Which of the rules of replacement states that, p ≡¬ (¬ p)

Group of answer choices

Double Negation

Associative laws

De Morgan's Law

none of the above

Double Negation

The number of wild animals in a zoo is not an example of a Discrete Data.

Group of answer choices

True

False

Which of the following criteria proves that your algorithms find the best solution.

Group of answer choices

Soundness

a. Termination

Optimality

Completeness

optimality

Ten apples is an example of a Continuous Data.

Group of answer choices

True

False

False

Which of the rules of replacement states that,

p ∨ c ≡ p

p ∧ t ≡ p

Group of answer choices

none of the above

Identity Law

De Morgan's Law

Commutative Law

Identity Law

It is a proposition in the form

"p if and only if q".

Group of answer choices

Disjunction

Biconditional

Conditional

Conjunction++

Biconditional

¬ (p ↔ q) is logically equivalent to ________

Group of answer choices

p↔¬q

q↔p

¬p↔¬q

¬q↔¬p

p↔¬q

By using Identity Law , is

p ∨ c ≡ p

True?

Group of answer choices

Yes

no

no

Choose a matching predicate logic for Everyone loves everyone

Group of answer choices

∀x∀y love (y, x)

all of the above

∀x∀y love (x, y)

p pp

Group of answer choices

True

False

https://docs.google.com/document/d/1G_TWqKCRRbVlUZUe-C5I4skcVTFuQNE9qaCe4yfzoHw/edit?usp=sharing

Which of the rules of replacement states that, Screen Shot 2020-07-05 at 2.05.45 AM.png

Group of answer choices

De Morgan's Law

Commutative Law

Distributive Law

Double Negation Law

https://docs.google.com/document/d/1G_TWqKCRRbVlUZUe-C5I4skcVTFuQNE9qaCe4yfzoHw/edit?usp=sharing

A declarative sentence that is either true or false, but not both.

Group of answer choices

Statement

Tautology

False

Contradiction

Statement

Which symbol is used for the Universal Quantifier, All?

Group of answer choices

none of the above

∧

∀

∃

∀

It is the science of necessary inference or study of reasoning

Group of answer choices

Truth Table

algorithm

logic

proposition

logic

It is a statement that is neither a tautology or a contradiction.

Group of answer choices

none of the above

Tautology

Contingency

Contradiction

Contingency

¬ (¬ p) is logically equivalent to?

Group of answer choices

¬ p

p v q

p

p → (q ∧ r)

p

p -> (p v q)is a tautology.

Group of answer choices

True

False

True

Which of the rules of replacement states that,

[p ∨ (q ∨ r)] ≡ [(p ∨ q) ∨ r]

[p ∧ (q ∧ r)] ≡ [(p ∧ q) ∧ r]

Group of answer choices

Double Negation

none of the above

De Morgan's Law

Associative law

Associative law

https://docs.google.com/document/d/1G_TWqKCRRbVlUZUe-C5I4skcVTFuQNE9qaCe4yfzoHw/edit?usp=sharing

contains image

The statement qconditional.p is logically equivalent to the statement qconditional.gif(pand.q).

Group of answer choices

True

False

False

By using Distributive Law, is

p ∨ (q ∧ r) ≡ (p ∧ q) ∨ (p ∧ r)

True?

Group of answer choices

no

Yes

Yes

Commutative Law states that (p ∧ q) is logically equivalent to _________.

Group of answer choices

none of the above

(q ∨ p)

(p ∨ q)

(q ∧ p)

(q ∧ p)

Associativity Law states that [p ∧ (q ∧ r)] is logically equivalent to __________.

Group of answer choices

[(p ∨ q) ∨ r]

[(p ∧ q) ∧ r]

[p ∨ (q ∨ r)]

none of the above

[(p ∧ q) ∧ r]

It is a relationship between two propositions where their truth tables are identical.

Group of answer choices

none of the above

Conditional

logical equivalence

biconditional

logical equivalence

∼ (p ∧ q) and ∼ p∨ ∼ q are logically equivalent.

Group of answer choices

True

False

True

Which of the following are logically equivalent?

Group of answer choices

none of the above

(p∧q)→p and (p∧q)→q

(p∧q)and(p∧q)→q

p∨q and q∧p

(p∧q)→p and (p∧q)→q

~qconditional_transp.gifp is logically equivalent to ~(pconditional_transp.gifq)

Group of answer choices

True

False

True