**Relationships of Equivalence and Logical Equations**

(1) Using the concept of mathematical equations (2 sides of an equation being in perfect, equal balance despite looking different), write an explanation describing why it can be helpful to study relationships of equivalence. Use the answer to this question as you formulate your lesson plan for this chapter.

(2) In what ways can writing and speaking in everyday language make argument translation difficult?

(3) Translate the following into a proposition in categorical form: *Anna wasn’t wearing any jewelry.* How does this sentence construction make translation difficult?

(4) Employing a different sentence construction, write an equivalent statement.

(5) Using the concepts of logical equivalence, explain why “No dogs are cats” AND “No cats are dogs” are both true, but “All dogs are mammals” is true, while “All mammals are dogs” is NOT true.

(6) Be contemplating the role of immediate inferences in obverse, converse, and contraposition conversions of propositions.