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- Intro to logic
- First-order logic
- Exercises for first-order logic
Determine whether the relation
on the set of all people is
reflexive,antireflexive,
symmetric,antisymmetric, and/or
transitive, where
if and only if …
-
is older than
.
-
is at least as old as
.
-
and
are exactly the same age.
-
and
have a common grandparent.
-
and
have a common grandchild.
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For each of the following, if the statement is true, explain why, and
if the statement is false, give a counter-example relation.
-
If
is reflexive,
then
is symmetric.
-
If
is reflexive,
then
is antisymmetric.
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If
is reflexive,
then
is not symmetric.
-
If
is reflexive,
then
is not antisymmetric.
-
If
is symmetric,
then
is reflexive.
-
If
is symmetric,
then
is antireflexive.
-
If
is symmetric,
then
is not antireflexive.
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Quantifiers
Let
be the statement
has been to Prague
,
where the domain consists of your classmates.
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Express each of these quantifications in English.
-
-
-
-
-
-
-
-
-
Which of these mean the same thing?
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Let
be the statement
has a cat
,
let
be the statement
has a dog
, and
let
be the statement
has a ferret
.
Express each of these statements in first-order logic usingthese relations.
Let the domain be your classmates.
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A classmate has a cat, a dog, and a ferret.
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All your classmates have a cat, a dog, or a ferret.
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At least one of your classmates has a cat and a ferret, but not a dog.
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None of your classmates has a cat, a dog, and a ferret.
-
For each of the three animals,
there is a classmate of yours that has one.
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Determine the truth value of each of these statements ifthe domain is all real numbers.
Where appropriate, give a witness.
-
-
-
-
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Let
,
,
, and
be the statements
is a duck
,
is one of my poultry
,
is an officer
, and
is willing to waltz
,
respectively.Express each of these statements using quantifiers, logical connectives,
and the relations
,
,
, and
.
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No ducks are willing to waltz.
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No officers ever decline to waltz.
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All my poultry are ducks.
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My poultry are not officers.
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Does the fourth item follow from the first three taken together?
Argue informally; you don't need to use thealgebra or inference rules for first-order logic here.
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You come home one evening
to find your roommate exuberant becausethey have managed to prove that there is an even prime number
bigger than two.More precisely, they have a correct proof of
,
for the domain of natural numbers,with
interpreted as
is prime?
and
interpreted as
is even?
.
While they are celebrating their imminent fame at thisamazing mathematical discovery, you ponder…
-
…and realize the formula is indeed true
for that interpretation.Briefly explain why.
You don't need to give a formal proof using Boolean algebra orinference rules; just give a particular value for
and explain why
it satisfies the body of
.
-
Is the formula still true when restricted to
the domain of natural numbers two or less?Briefly explain why or why not.
-
Is the formula still true when restricted to the empty domain?
Briefly explain why or why not.
-
Give a formula that correctly captures the notion
there is an even prime number bigger than 2
.
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Questions & Answers
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
Lambiv
how is the graph works?I don't fully understand
hi guys good evening to all
Lambiv
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
Can I ask you other question?
Shukri
What is different between quantity demand and demand?
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
how do you save a country economic situation when it's falling apart
what is the difference between economic growth and development
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
any question about economics?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:
OpenStax, Intro to logic. OpenStax CNX. Jan 29, 2008 Download for free at http://cnx.org/content/col10154/1.20
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