Let p (x, y) be the statement "student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer science courses at your school. express each of these quantifications in english.
a) ∃x∃yp (x, y)
b) ∃x∀yp (x, y)
c) ∀x∃yp (x, y)
d) ∃y∀xp (x, y)
e) ∀y∃xp (x, y)
f) ∀x∀yp (x, y)

Hello mate!

we know that p(x,y) means "Student x has taken class y"

and the used symbols are:  

∃: this means "existence", you use this symbol to say that there exists at least one object that makes true the sentence.

∀: this means "for all", you use this symbol to say that the sentence is true for all the elements, then:

a) ∃x∃yP (x, y)

"exist at least one student x, that took at least one class y"

b) ∃x∀yP (x, y)

"exist at least one student x, that took all the classes y"

c) ∀x∃yP (x, y)

"every student x, took at least one class y"

d) ∃y∀xP (x, y)

"exist at least one class y, that has been taken by all the students x"

e) ∀y∃xP (x, y)

"for every class y, there is at least one student x that took the class"

f) ∀x∀yP (x, y)

"all the students x took all the classes y"

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: