Foundations of Advanced Mathematics
Material on Test 1 (Friday, September 23)
Sec. 1.1. Propositions; and, or, not; truth tables; denials; tautologies and contradictions.
Sec. 1.2. "If then" and "if and only if"; denials; converse, contrapositive.
Sec. 1.3. "For all," "there exists," and "there exists a unique"; translation between English and symbolic sentences; denials.
Sec. 1.4. Direct proof; proof by cases.
Sec. 1.5. Contrapositive proofs; proof by contradiction.
Sec. 1.6. Proofs involving "for all" and "there exists."
Possible subjects of proofs: even and odd numbers, what divides what, rational and irrational numbers, absolute value.
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