3. Suppose the variable x represents students, and

F(x) means x is a freshman, M(x) means x is a math major.

Translate the following English statements into logic using the given predicates and any needed quantifiers:

a) Some freshmen are math majors.

b) Every math major is a freshman.

c) No math major is a freshman.

4. Suppose the variable x represents people, and

F(x): x is friendly T(x): x is tired H(x): x is happy.

Translate the following predicate logic statements into English.

a) T(Bob).

b) x (T(x) H(x)).

c) x (F(x) H(x)).