Negating the Nested Quantifiers (Example 3)

Discrete Mathematics: Negating the Nested Quantifiers.
Topics discussed:
1) Solved example on negating the nested quantifiers.

Music:
Axol x Alex Skrindo - You [NCS Release]

#DiscreteMathematicsByNeso #DiscreteMaths #NestedQuantifiers

[yashagrawal]

Answer: ∀x ∃y ~T(x, y)
For Every Student in this class there exist at least one mathematics course such that no one has taken the course
OR
None of the students in this class has taken all mathematics courses offered at this school.

[acriziosouza]

Solution:

Domain of x: "all students in this class."
Domain of y: "all mathematical courses offered at this school."

T(x, y) = x has taken y mathematical courses offered at this school

∃x ∀y T(x, y)

Negation: ∀x ∃y ¬T(x, y)

Translation:
Every student in this class has not taken every mathematical course offered at this school

OR

For every student in this class, there exist at least one course that no one has taken it.

[_rajeshkumar]

Huge respect sir for these kind of work

[bhupeshpattanaik]

a video on backtracking, plz teach as you taught in recursions i.e. using stacks that was a wonderful explanation

[DeepakKumar-nkcv]

Sir huge request to upload data structure videos daily...🙏🙏🙏

[soorya_k]

Every student in this class who has not taken some mathematics course offered at this school

[gamexd]

ans. - ∃x ∀y T(x, y) [if T(x, y) = x has taken y mathematics courses in this school]
negation - ∀x ∃y ~T(x, y)
English - For Every Student in class There Exist at least one mathematics course such that no one has taken the course
If Any Mistake Please

[rahulverma]

Answer: ∃x ∀y Taken(x, y)
where x is student and y is mathematics course

[aparnasamal]

Every students in the class have not taken some mathematics courses offered at the the school

[rajeshprajapati]

Answer to H.W. : Negation: ∀x ∃ y ¬(T(x, y))
Every student in this class has not taken a mathematics course offered at this school.

[gowriv]

Sir please upload the control system vedios.

[rohithpamidimarri]

in this video at 2.00/2.36 while negating the negation is not kept for c(x, y) can anyone pls explain that?

[vilmil]

We are speaking about both "Class" And "School", so we should consider "School" as our domain and use a predicate such as C(x) for "x is in class", also we should consider below predicates and domains:

Domain of x is all students in school and domain of y is all courses offered at this school

T(x, y): student x has taken course y.

M(y): y is a mathematics course.

Negation using Quantifiers: ∀x(¬C(x) ∨ ∃y(Math(y) ∧ ¬T(x, y)))

Negation in English: every student is not in this class or there is a mathematics course which is not taken by the student.

[nutankumbhar]

please upload the videos for the correct answer thank you

[vinayakf]

All students are not enrolled in some courses .

[saisrikantta]

No student has taken every mathematics course offered at this school

[firozansari]

No one student has taken at least one math course offered by this school. ∀x∃y¬T(x, y)

[prabhattripathi]

every student in this class has not taken some mathematics course offered at this school.

[dusuruhemanthsaikiran]

no student has taken every math course offered in this school (~ ∃x ∀y f(x, y))

[nutankumbhar]

∃x∀yt(x, y) and the negation is ∃x∀y¬t(x, y)