Stage 35 · Logic & Quantifiers

35.5.2 Putting Equivalent Statements to Work

35.5 Simple Logical Reasoning

Point 2 of 5

35.5.2 Putting Equivalent Statements to Work

Core idea

When the direct proof is hard, prove the contrapositive instead: switch to an equivalent phrasing and the path often clears at once.

Module goal. Link conditions, quantifiers, and negation into reasoning — using counterexamples, the contrapositive, and proof by contradiction — and pave the way for rigorous arguments about sequences and function limits.

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