a. There is a student who has seen Casablanca. b. All students have seen Star Wars. c. Every student has seen at least one movie. d. There is a movie that has been seen by every student. e. There are two different students who have seen the same movie. f. Every movie that a particular student has seen, has also been seen by another student.
Work Step by Step
Recall other ways to express the symbol $\forall$ include: for all, for every, for any, for each, for arbitrary, given any. Other ways to express the symbol $\exists$ include: there exists, there exist, there exists at least one, for some, for at least one, we can find a. When a statement contains more than one quantifier, we imagine the actions suggested by the quantifiers as being performed in the order in which the quantifiers occur.