Prposition logic | Computer Science homework help

The following quiz must be completed

 

Question 1

Not yet answered

Marked out of 100

Flag question

Question text

Which of these statements are true, for propositional logic? (In an exam you would have to justify your answers).

Select one or more:

A. If a formula is not satisfiable then it is not valid

B. X is not satisfiable if and only if ¬X is valid

C. If a formula is not valid then it is not satisfiable

D. X is not valid if and only if not X is satisfiable

Question 2

Not yet answered

Marked out of 100

Flag question

Question text

For each propositional formula below, construct a truth table. Which formulas are valid?

Select one or more:

A. (prightarrow p)

B. p

C. (pwedge q)

D. ((prightarrow(qvee r)) leftrightarrow((prightarrow q)vee(prightarrow r)))

E. (prightarrow(qrightarrow p))

Question 3

Not yet answered

Marked out of 100

Flag question

Question text

In each case say if the formula is satisfiable.

Select one or more:

A. neg(prightarrow(qrightarrow p))

B. p

C. neg((prightarrow q)rightarrow p)

D. (pwedge q)

E. (pwedgeneg p)

Question 4

Not yet answered

Marked out of 100

Flag question

Question text

Which of the following sets of connectives are functionally complete for propositional logic?

Select one or more:

A. wedge, vee, neg

B. rightarrow, bot (false)

C. vee, neg

D. wedge, vee

E. rightarrow, wedge

Question 5

Not yet answered

Marked out of 100

Flag question

Question text

Which of the following are propositional formulas, according to the strict definition of propositional formulas?

Select one or more:

A. neg(p)

B. prightarrow q

C. (pwedge q)

D. ((prightarrow q)rightarrow p)

E. (pwedge qwedge r)

Question 6

Not yet answered

Marked out of 100

Flag question

Question text

Consider the following 11 propositional formulas

  1. (prightarrow(qrightarrow p))

  2. (q rightarrow p)

  3. ( neg p vee  q )

  4. (neg p wedge neg q )

  5. (p vee neg p )

  6. (p vee neg q )

  7. ((p veeneg q) wedge (neg p vee q))

  8. (p wedgeneg p)

  9. (p rightarrow  q)

  10. ((p wedge neg q) vee (neg p wedge  q))

  11. (p leftrightarrow  q)

Which of these eleven formulas are equivalent to each other. Choose one from the following:

Select one:

A. 1=5, 2=3, 7=11, 4=10, 6=9

B. None of the other answers are right

C. 1=5, 2=6, 3=9, 7=11

D. 1=5, 2=6, 4=7=10, 3=9

E. None are equivalent

Question 7

Not yet answered

Marked out of 100

Flag question

Question text

Which of the following propositional formulas are in disjunctive normal form?

Select one or more:

A. neg p

B. (p veeneg q)

C. ((p veeneg q) wedge r)

D. ((p wedge q) vee (neg p wedgeneg q))

E. ((neg p wedge q) vee (p wedge neg q))

Question 8

Not yet answered

Marked out of 100

Flag question

Question text

Which of the following statements is true?

Select one or more:

A. There is a DNF formula which is equivalent to all possible propositional formulas.

B. There is no DNF formula equivalent to (p wedgeneg p)

C. For every propositional formula there is a CNF formula equivalent to it.

D. For every propositional formula there is a DNF formula equivalent to it.

Question 9

Not yet answered

Marked out of 100

Flag question

Question text

Let i be the propositional valuation where i(p) = t, i(q) = t, i(r) = f, …

Let v be the truth function that extends i. Which of the formulas below evaluate to true under this valuation v?

Select one or more:

A. (((p leftrightarrow q) rightarrowneg(p wedgeneg r)) veeneg r )

B. (neg p rightarrow (q wedgeneg p))

C. (p wedgeneg r)

D. (neg p rightarrow q)

Question 10

Not yet answered

Marked out of 100

Flag question

Question text

Let L be a first order language with just one predicate, =, and no constants or function symbols. Let An be a sentence that is true in a structure M if and only if M has at least n points in its domain. What is the smallet number of variables required to write such a sentence An?

Select one:

A. 2

B. n

C. n-1

D. 1

E. infinity

Question 11

Not yet answered

Marked out of 100

Flag question

Question text

Let S=({mathbb N}, I) where I(<^2) is the set of all (x, y) where x is strictly less than y, constants 0, 1 denote zero and one respectively.  Which of the following first order formulas are true in the structure S?

Select one or more:

A. forall xexists y <^2(x, y)

B. neg (<^2(0, 1)rightarrow(0=+^2(0, 1)))

C. <^2(1, +^2(1, 0))

D. forall xexists y <^2(y, x)

E. (<^2(1, +^2(0, 0))vee (1=+^2(0, 1)))

Question 12

Not yet answered

Marked out of 100

Flag question

Question text

Let S be the structure ({mathbb N}, I)  where the domain is the set of natural numbers and  I(<) is the set of pairs (x, y) where x is strictly less than y. Using S and the assignments A1 to A5 below, say which of the following are true.

A1:

x -> 7

y -> 14

z -> 9

w -> 5 (all other vars w)

 

A2:

x -> 8

y -> 7

z -> 9

w -> 5 (all other w)

 

A3:

x -> 0

y -> 14

z -> 9

w -> 5 (all other w)

 

A4:

x -> 8

y -> 14

z -> 9

w -> 5 (all other w)

 

A5:

x -> 6

y -> 14

z -> 9

w -> 5 (all other w)

Select one or more:

A. S, A1 |= small exists x <^2(x, 1)

B. S, A1 |= small forall xexists y <^2(x, y)

C. S, A3 |= small <^2(x, 1)

D. S, A2 |= small <^2(x, 1)

E. S, A2 |= small negexists z(<^2(y, z)wedge <^2(z, x))

Question 13

Not yet answered

Marked out of 100

Flag question

Question text

Let L be a first-order language with just = as a predicate and no constants or function symbols. How many variables to you need to express a sentence that is true in a model if and only if the domain has exactly n elements?

Select one:

A. 2

B. n+1

C. n

D. n-1

E. 2n+1

Question 14

Not yet answered

Marked out of 100

Flag question

Question text

In the following formula > means greater than, = means equals, * means times. Which statement below is a good translation of the first order formula?

small forall x[neg(exists yexists z(x=y*zwedge y>1wedge z>1))rightarrowexists w(w>xwedgeneg(exists yexists z(w=y*zwedge y>1wedge z>1)))]

 

Select one:

A. for every composite number there is a prime number

B. for every prime number there is a bigger prime number

C. x and w are prime numbers

D. all numbers bigger than x are prime.

E. for all x, if x is a prime number then w is a prime number.

Question 15

Not yet answered

Marked out of 100

Flag question

Question text

Consider the first order formula:

small (forall x(exists y P^2(x, y)rightarrow R^2(y, x))rightarrow Q^1(x))

Which statements are correct?

Select one or more:

A. The scope of small forall x is small ((exists y P^2(x, y)rightarrowexists x R^2(y, x))rightarrow Q^1(x))

B. the scope of small exists y is small P^2(x, y)

C. small R^2(y, x) is in the scope of small exists x and small exists y, but not in small forall x.

D. there is one free occurence of small x: the small x in small Q^1(x)

E. This is not a well-formed formula.

Question 16

Not yet answered

Marked out of 100

Flag question

Question text

Take a first order language with constants C = {0,1}, predicates P = {R^2} and functions F = {+^2, -^1, times^2}.

Which of the following are terms in this language?

Select one or more:

A. +^2(x, y, 1)

B. times^2(+^2(0, 1), +^2(0, 1))

C. R^2(x, 0)

D. -^1(0, 1)

E. +^2(3, 0)

Question 17

Not yet answered

Marked out of 100

Flag question

Question text

Let S be the structure ({mathbb N}, I)  where I(<) is the set of pairs (x, y) where x is strictly less than y.Which of these first order formulas are valid in S?

Select one or more:

A. exists xforall y(<^2(x, y)vee (x=y))

B. forall yexists x(<^2(x, y)vee (x=y))

C. forall xforall y((<^2(x, y)vee <^2(y, x))vee x=y)

D. forall yexists x <^2(y, x)

E. exists xforall y <^2(y, x)

Question 18

Not yet answered

Marked out of 100

Flag question

Question text

Which of these first order formulas are valid?

Select one or more:

A. (forall xneg R^1(x) rightarrownegexists x R^1(x))

B. (exists xforall y <^2(x, y)rightarrow forall yexists x <^2(x, y))

C. forall xforall y ((<^2(x, y)vee <^2(y, x))vee(x=y))

D. (forall xexists y <^2(x, y) rightarrow exists yforall x <^2(x, y))

Question 19

Flag question

Question text

Predicate Logic. Consider the following assignments.

A1:

x -> 7

y -> 14

z -> 9

w -> 5 (all other vars w)

 

A2:

x -> 8

y -> 7

z -> 9

w -> 5 (all other w)

 

A3:

x -> 0

y -> 14

z -> 9

w -> 5 (all other w)

 

A4:

x -> 8

y -> 14

z -> 9

w -> 5 (all other w)

 

A5:

x -> 6

y -> 14

z -> 9

w -> 5 (all other w)

 

Which statements are correct?

Select one or more:

A. A1 is an x-variant of A3

B. A5 is a z-variant of A5

C. A4 is a z-variant of A5

D. A2 is a y-variant of A4

E. A3 is an x-variant of A5

Question 20

 

Question text

Let S be the structure ({mathbb N}, I)  where I(<) is the set of pairs (x, y) where x is strictly less than y, I(+) is the ordinary addition function, I(0), I(1) are the integers zero, one respectively..Using the structure S  calculate the interpretation of

+2(+2(1,1), +2(0,1))

Answer:

Question 21

Let S be the structure ({mathbb N}, I)  where I(<) is the set of pairs (x, y) where x is strictly less than y. Let A be the assignment where x -> 5 and y -> 8.

Calculate [+ 2(x, y)]S,A

Answer:

 

 

 

 

 

Calculate your paper price
Pages (550 words)
Approximate price: -

Why Choose Us

Quality Papers

We value our clients. For this reason, we ensure that each paper is written carefully as per the instructions provided by the client. Our editing team also checks all the papers to ensure that they have been completed as per the expectations.

Professional Academic Writers

Over the years, our Acme Homework has managed to secure the most qualified, reliable and experienced team of writers. The company has also ensured continued training and development of the team members to ensure that it keep up with the rising Academic Trends.

Affordable Prices

Our prices are fairly priced in such a way that ensures affordability. Additionally, you can get a free price quotation by clicking on the "Place Order" button.

On-Time delivery

We pay strict attention on deadlines. For this reason, we ensure that all papers are submitted earlier, even before the deadline indicated by the customer. For this reason, the client can go through the work and review everything.

100% Originality

At Papers Owl, all papers are plagiarism-free as they are written from scratch. We have taken strict measures to ensure that there is no similarity on all papers and that citations are included as per the standards set.

Customer Support 24/7

Our support team is readily available to provide any guidance/help on our platform at any time of the day/night. Feel free to contact us via the Chat window or support email: support@acmehomework.com.

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

Papers Owl has stood as the world’s leading custom essay writing services providers. Once you enter all the details in the order form under the place order button, the rest is up to us.

Essays

Essay Writing Services

At Papers Owl, we prioritize on all aspects that bring about a good grade such as impeccable grammar, proper structure, zero-plagiarism and conformance to guidelines. Our experienced team of writers will help you completed your essays and other assignments.

Admissions

Admission and Business Papers

Be assured that you’ll definitely get accepted to the Master’s level program at any university once you enter all the details in the order form. We won’t leave you here; we will also help you secure a good position in your aspired workplace by creating an outstanding resume or portfolio once you place an order.

Editing

Editing and Proofreading

Our skilled editing and writing team will help you restructure you paper, paraphrase, correct grammar and replace plagiarized sections on your paper just on time. The service is geared toward eliminating any mistakes and rather enhancing better quality.

Coursework

Technical papers

We have writers in almost all fields including the most technical fields. You don’t have to worry about the complexity of your paper. Simply enter as much details as possible in the place order section.

See all services
error: Content is protected !!