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... of chalk and tapped it against the blackboard while writing about set theory.

The concept of sets.

Sufficient and necessary conditions.

Truth values of propositions.

The three types of propositions: converse, inverse, and contrapositive.

The students below were all listening attentively.

Whether they actually understood or not was another matter.

At the back of the classroom by the window, Takashi twirled his pen as he followed along with t ...

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