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Mathematics
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Module 1
Language and Methods of Proof
1
Translating Between Quantified Statements and Precise Prose
Translate mathematical statements between quantified symbolic form and precise prose.
Translate mathematical statements between quantified symbolic form and precise prose.
2
Negating Universal and Existential Quantifiers
Negate statements containing universal and existential quantifiers.
Negate statements containing universal and existential quantifiers.
3
Disproving Universal Statements with Counterexamples
Disprove a universal statement by constructing a counterexample.
Disprove a universal statement by constructing a counterexample.
4
Direct Proof from Definitions and Hypotheses
Prove an implication directly from definitions and stated hypotheses.
Prove an implication directly from definitions and stated hypotheses.
5
Proving Implications by Contraposition
Prove an implication by contraposition.
Prove an implication by contraposition.
6
Proof by Contradiction
Prove a statement by contradiction.
Prove a statement by contradiction.
7
Proving Formulas and Divisibility by Mathematical Induction
Prove a formula or divisibility statement by mathematical induction.
Prove a formula or divisibility statement by mathematical induction.
8
Proving a Function Is Bijective: Injectivity and Surjectivity
Prove that a specified function is bijective by establishing injectivity and surjectivity.
Prove that a specified function is bijective by establishing injectivity and surjectivity.
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