1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ryzh [129]
3 years ago
15

Translate each statement into a logical expression. Then negate the expression by adding a negation operation to the beginning o

f the expression. Apply De Morgan's law until each negation operation applies directly to a predicate and then translate the logical expression back into English.
Sample question: Some patient was given the placebo and the medication.
∃x (P(x) ∧ D(x))
Negation: ¬∃x (P(x) ∧ D(x))
Applying De Morgan's law: ∀x (¬P(x) ∨ ¬D(x))
English: Every patient was either not given the placebo or not given the medication (or both).
(a) Every patient was given the medication.
(b) Every patient was given the medication or the placebo or both.
(c) There is a patient who took the medication and had migraines.
(d) Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p → q ≡ ¬p ∨ q.)
Computers and Technology
1 answer:
kotegsom [21]3 years ago
6 0

Answer:

P(x): x was given the placebo

D(x): x was given the medication

M(x): x had migraines

Explanation:

(a) Every patient was given the medication

Solution:

∀x D(x)

∀ represents for all and here it represents Every patient. D(x) represents x was given the medication.

Negation: ¬∀x D(x).

This is the negation of Every patient was given the medication.

The basic formula for De- Morgan's Law in predicate logic is:

¬(P∨Q)⇔(¬P∧¬Q)

¬(P∧Q)⇔(¬P∨¬Q)

Applying De Morgan's Law:

          ∃x ¬D(x)

∃ represents there exists some. As D(x) represents x was given the medication so negation of D(x) which is ¬D(x) shows x was not given medication. So there exists some patient who was not given the medication.

Logical expression back into English:

There was a patient who was not given the medication.

(b) Every patient was given the medication or the placebo or both.

Solution:

∀x (D(x) ∨ P(x))

∀ represents for all and here it represents Every patient. D(x) represents x was given the medication. P(x) represents  x was given the placebo . V represents Or which shows that every patient was given medication or placebo or both.

Negation: ¬∀x (D(x) ∨ P(x))

This is the negation or false statement of Every patient was given the medication or the placebo or both.

Applying De Morgan's Law:

∃x (¬D(x) ∧ ¬P(x))

∃ represents there exists some. As D(x) represents x was given the medication so negation of D(x) which is ¬D(x) shows x was not given medication. As P(x) represents x was given the placebo so negation of P(x) which is ¬P(x) shows x was not given placebo. So there exists some patient who was neither given medication nor placebo.

Logical expression back into English:

There was a patient who was neither given the medication nor the placebo.

(c) There is a patient who took the medication and had migraines.

Solution:

∃x (D(x) ∧ M(x))

∃ represents there exists some. D(x) represents x was given the medication. M(x) represents x had migraines.  ∧ represents and which means patient took medication AND had migraines. So the above logical expression means there exists a patient who took medication and had migraines..

Negation:

¬∃x (D(x) ∧ M(x))

This is the negation or false part of the above logical expression: There is a patient who took the medication and had migraines.

Applying De Morgan's Laws:

∀x (¬D(x) ∨ ¬M(x))

∀ represents for all. As D(x) represents x was given the medication so negation of D(x) which is ¬D(x) shows x was not given medication. As M(x) represents x had migraines so negation of ¬M(x) shows x did not have migraines. ∨ represents that patient was not given medication or had migraines or both.

Logical expression back into English:

Every patient was not given the medication or did not have migraines or both.

(d) Every patient who took the placebo had migraines.

Solution:

∀x (P(x) → M(x))

∀ means for all. P(x) represents  x was given the placebo . M(x) represents x had migraines. So the above logical expressions represents that every patient who took the placebo had migraines.

Here we are using conditional identity which is defined as follows:

Conditional identity, p → q ≡ ¬p ∨ q.

Negation:

¬∀x (P(x) → M(x))

¬∀ means not all. P(x) implies M(x). The above expression is the negation of Every patient who took the placebo had migraines. So this negation means that Not every patient who took placebo had migraines.

Applying De Morgan's Law:

∃x (P(x) ∧ ¬M(x))

∃ represents there exists some.  P(x) represents  x was given the placebo . ¬M(x) represents x did not have migraines. So there exists a patient who was given placebo and that patient did not have migraine.

Logical expression back into English:

There is a patient who was given the placebo and did not have migraines.

You might be interested in
Which consol was dominant in the US market between 1993 and 1998
Illusion [34]

i believe the Nintendo 64

8 0
3 years ago
Introduction or background of corporal punishment in schools
tensa zangetsu [6.8K]

Answer:

Corporal punishment is a discipline method in which a supervising adult, such as a teacher, deliberately inflicts pain upon a child in response to a child's unacceptable behavior or inappropriate language. The goals of this type of punishment are usually to halt the offense immediately, prevent it from happening again, and set an example for others.

3 0
3 years ago
As Jason walks down the street, a large raven starts squawking at him and flapping its wings. Jason thinks to himself ‘That bird
UNO [17]

Answer:

Answer to the following question is anthropomorphism.

Explanation:

Anthropomorphism is considered as the error in the following context of the scientific reductionism. Anthropomorphize is the source of an error that needs to reconsider.

Anthropomorphism is an attribute of the human qualities, emotions, thoughts, motivation, intentions, and characteristics to the non-living beings or the nonhuman beings, things or objects.

8 0
3 years ago
Transistors contain a huge number of integrated circuits <br><br> a. true or <br> b. false
malfutka [58]
False. Integrated circuits have transistors within them, not the other way around
6 0
3 years ago
Which option can you use to control how text flows around a graphic?
Art [367]

Answer:

I believe your answer is C: Wrap Text

Explanation:

If you are trying to put an image in a more specific placement you would use Wrap Text. It helps making the image more clear and understandable because without wrapping the text it wouldnt make any sense and it would just be plain.

Hope this helps

3 0
3 years ago
Read 2 more answers
Other questions:
  • The LTE (cellular telephone) standard supports only packet switching"". What cellular services are morst affected by this change
    15·1 answer
  • Nonvolatile in the context of data storage means ________________. a. the data can't be changed in a data warehouse. b. the data
    11·1 answer
  • You and your friend play a video game where a superbird has to find and eat radiation leaks at nuclear power plants before the p
    13·2 answers
  • Which two encryption protocols might be used to provide secure transmissions for browser and web server communications?
    14·1 answer
  • Suppose x and y are int variables and ch is a char variable. Consider the following input: 5 28 36 What value (if any) is assign
    11·1 answer
  • 5 of 10
    7·1 answer
  • If I wanted to repeat an action such as a heading for a paper, it would be helpful to _____. create a citation create a caption
    9·2 answers
  • Good Morning! Please Help!
    15·1 answer
  • Assume there is an interactive math tutor. Many students take the math lessons online. At the end of each lesson, students have
    5·1 answer
  • All Office programs have similar commands on the tab for changing the document view a. File b. View c. Locate d. display ​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!