Let S be the set of students at your school, let M be the set of movies that have ever bee...

Let S be the set of students at your school, let M be the set of movies that have ever been released, and let V (s, m) be “student s has seen movie m.” Rewrite each of the following statements without using the symbol ∀, the symbol ∃, or variables.

a. ∃s ∈ S such that V(s, Casablanca).

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b. ∀s ∈ S, V(s, Star Wars).

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c. ∀s ∈ S, ∃m ∈ M such that V (s, m).

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d. ∃m ∈ M such that ∀s ∈ S, V (s, m).

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e. ∃s ∈ S, ∃t ∈ S, and ∃m ∈ M such that s ≠ t and V(s, m)  V(t, m).

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f. ∃s ∈ S and ∃t ∈ S such that s ≠ t and ∀m ∈ M, V(s, m) → V(t, m).