# (8 pts) 7. Identify which of the following (if any) are tautologies regardless of P, Q and the universe of discourse for x….

Identify which of the following are tautologies….

Don't use plagiarized sources. Get Your Custom Essay on
(8 pts) 7. Identify which of the following (if any) are tautologies regardless of P, Q and the universe of discourse for x….
Get an essay WRITTEN FOR YOU, Plagiarism free, and by an EXPERT!

Apparently a. and d. are tautologies, but I cannot understand why so I do not know how to prove either.

(8 pts) 7. Identify which of the following (if any) are tautologies regardless of P, Q and the universe of discourse for x. If the statement is a tautology prove it. Be sure to state all laws or rules of inference that you use in your proof. b. axPOx) A3xQ(x) 3x(P(x), A, Q(x))

For all iplication rules we need to test for only one case,when left hand side of the implication is 1 and right hand side is 0 that will result false.

a)
LHS: this is true only when there exist x (let it be x1) for which both P(x) and Q(x) holds true (i.e. P(x1) = true, and Q(x1) = true)

RHS: If LHS is true, we cannot make LHS false (since we have atleast one x, for which both P() and Q() are true. So obhiously there exist a x for which P() is true and there exist a x for which Q() is true)

So this is Tautology

b)
LHS: This is true when there exist a x (let it be x1) for which P(x) is true and there exist a x,may be different, (let it be x2) for which Q(x) is true.

RHS: If LHS is true, we cannot be sure RHS is true, because RHS demands there exist x (let it be x1) for which both P(x) and Q(x) holds true (i.e. P(x1) = true, and Q(x1) = true)

so this is not Tautology

c)
LHS: is True when for all x either P(x) is true or Q(x) is true.

RHS: If LHS is true we cannot comment on RHS, since RHS demands for all x P(x) is true or for all x Q(x) is true. (difference is in LHS it states that we can have x1 such that P(x1) is false, but Q(x1) should be true or vice-versa. But RHS says either P(x) is true for all X or Q(x) is true for all X)
so this is not Tautology

d)
LHS:This is true if for all x P(x) is true or for all x Q(x) is true.

RHS:True value of LHS confirms RHS is True because RHS demands for all x either P(x) is true or Q(x) is true.

so this is Tautology

I hope you like the explanation provided. If you have and doubt please feel free to comment below. I shall be glad yo help you

Order NOW For a 10% Discount!
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

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

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.