Logo
Home Study Material Contact Search
AI Chat FREE
  1. business
  2. accounting
  3. let x1,...,xn be variables, a formula, t a term,

Let x1,...,xn be variables, a formula, t a term, and t1,...,tn terms. We define...

70.2K

Verified Solution

Question

Accounting

Let x1,...,xn be variables, a formula, t a term, and t1,...,tn terms. We define t(t1/x1, . . . , tn/xn) to be the expression obtained by replacing occurrences of x1, . . . , xn simultanously by t1, . . . , tn, and similarly let (t1/x1, . . . , tn/xn) be the expression that is obtained by replacing free occurrences of x1, . . . , xn in simultaneously by t1, . . . , tn.

(a) Show that t(t1/x1, . . . , tn/xn) is a term.

(b) Show that for any structure M and any tuple a from M we have

tM(t1/x1, . . . , tn/xn)(a) = tM(b), where b is the tuple that is obtained by replacing the ith component of a by tMi (a)

for each i {1,...,n}.

(c) Show that (t1/x1, . . . , tn/xn) is a formula.

(d) Suppose that ti is free for xi in for each i. Show that for any structure M and any tuple a from M we have that

M |= (t1/x1, . . . , tn/xn)(a) M |= (b), where b is defined as in part (b).

Answer & Explanation Solved by verified expert
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Geometry
1.2K views

14 Classify each angle as right obtuse or acute A

Psychology
1.2K views

What is 'existentialism'? Which philosophers are existentialists that you read about?

Psychology
1.2K views

Can you think of a time when you conformed with the actions of a group of friends,...

General Management
1.2K views

Airlines are comprised of many types of aircraft within their fleet to accomplish the route structure...

Advance Math
1.2K views

let G be a simple graph. show that the relation R on the set of vertices of...

Basic Math
1.2K views

Give the expected value, variance, and probability distribution for the sum of a fair coin and...

Biology
1.2K views

Accessing information legally Crediting creators of information appropriately Return 1 point According to the tutorial...

Statistics
1.2K views

Determine whether the following procedure results in a binomial distribution or a distribution that can...

Calculus
1.2K views

Without a calculator match each function with its graph y log x e ba y...

Accounting
1.2K views

Perrot industries has $355,000 to invest. The company is trying to decide between two alternative...

Accounting
1.2K views

Exercise 10-12A Prepare a statement of stockholders' equity (LO10-7) Power Drive Corporation designs and produces...

Accounting
1.2K views

need help turning this information into a t account. Equity: -...