Answer:
See the table attached for complete solution to the problem.
∃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.)
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.
Answer:
Well, I am studying software engineering and ethical hacking, with the terms I mentioned it is very self explanatory how I use computers for those fields. In case it is still not self explanatory, we use computers to make software and websites accessing tools that can only be access using a computer and a working internet connection is required. Ethical hacking requires a computer to test the website or application security in order to do that we need a active internet connection in order to access the website itself.
Explanation:
i dont really know i am not really sure what i qill be in the future
Answer:
hybrid topology
Explanation:
The type of topology that is being described is known as a hybrid topology. Like mentioned in the question this is an integration of two or more different topologies to form a resultant topology which would share the many advantages and disadvantages of all the underlying basic topologies that it is made up of. This can be seen illustrated by the picture attached below.
b) Within that file only
c) global
Answer:
The correct answer for the given question is option(a) i.e Local - within that function.
Explanation:
The variable which is declared inside any function are called as local variable The scope and lifetime of local variable is inside that block or function only.
They cannot access outside the function.
Following are the example of local variable
#include <stdio.h> // header file
void fun(); // function prototype
int main()// main function
{
fun(); //calling function
print("%d",t); // it gives error because t is local variable cannot access in main function
return 0;
}
void fun()
{
int t=9;// local variable
printf("t is local variable which value is:");
printf("%d",t);
}
As we seen that t cannot access outside the function .So correct answer is option(a)
The scope of a variable declared inside of a function is local - within that function. This prevents naming conflicts and ensures control over where a variable can be changed.
The scope of a variable declared inside of a function is typically local to that function. This means that it can only be accessed and manipulated within the function it is declared. It is not visible or accessible from outside of the function or elsewhere in the program file, hence options b) and c) are incorrect. This principle is fundamental in programming languages such as JavaScript, C++, Python, etc., and it is designed this way to prevent naming conflicts and provide control over where a variable can be changed.
#SPJ6
b. fork
c. break
d. loop
Answer:
Option D is correct.
Explanation:
A Loop statment is a control flow statement that repeatedly executes a statement or a series of statements while the value of a specific condition is truthy or until the value of a specific condition becomes truthy.