Let S(x, y) denote the statement "x has seen y" and D denote the set of all students in our class and M be the set of all movies. a. Express the following English sentence as a quantified proposition using the definitions above:
"For every movie there is a pair of students in our class who have both seen it." Hint: Use three quantifiers - one for the movie and two for a pair of students.

b. Negate the quantified proposition you wrote for part (a) (i. e., place a "¬" in front of it). Use de Morganâs law for quantifiers to move the negation inside the quantifiers.
c. Translate you answer for part (b) back to plain English.

Step-by-step explanation:

a) Recall the quantifiers .

Then, we can translate the proposition as follows

b) Recall that an expression of the form its negation is of the form which means that it is not true that for all elements the proposition P holds. Equivalently, we have that the negation of an expression of the form is which means that there is at least one x such that P doesn't hold. Using this, we get the following

By De Morgan's law, we have that

So, the final statement is

c)

This statement means: There is a movie that for every pair of students, at least one of the students hasn't seen the movie yet.

10000000000000000000000000000000

answer:

your answer is: c. 196 7/8 in^3.