Proof by Contradiction, Contrapositive, and Disproof by Counterexample

7 lessons

Goal

Master indirect proof methods including contradiction, contraposition, and finding minimal counterexamples to refute conjectures.

Logical Equivalence of Conditional and Contrapositive Statements

7 lessons

0 of 7 done

Logical Equivalence of Conditional and Contrapositive StatementsUp next
The Structure of Proof by Contradiction: Setting up the NegationPremiumNot started yet
Proving the Irrationality of Square Roots by ContradictionNot started yet
Proving the Irrationality of Logarithms and Sums of SurdsNot started yet
Euclid's Proof of the Infinitude of Prime NumbersNot started yet
Disproof by Counterexample for Universally Quantified StatementsNot started yet
Evaluating Proof Validity and Identifying Logical FallaciesNot started yet

Standards Covered

Curriculum Framework

7 lessons

Construct direct algebraic proofs, deductions from axioms, and proofs by exhaustion for finite cases and number-theoretic properties.

7 lessons

Master indirect proof methods including contradiction, contraposition, and finding minimal counterexamples to refute conjectures.

6 lessons

Analyze the topological structure of the real line, including Archimedean property, density of rationals, and the completeness axiom.

6 lessons

Manipulate complex surd expressions, apply index laws across all rational exponents, and rationalize multi-term radical denominators.

8 lessons

Perform arithmetic on complex numbers in Cartesian form, compute modulus and conjugates, and graph loci in the Argand diagram.

7 lessons

Convert between Cartesian, polar, and Euler's exponential forms, compute products and quotients, and evaluate powers via De Moivre's Theorem.

8 lessons

Apply the Fundamental Theorem of Algebra, factor polynomials completely over the complex numbers, and solve higher-degree equations.