Use precise definitions before starting any proof
Identify the logical form of the statement
Translate words into symbols
Determine whether the statement is universal, existential, conditional, or biconditional
Choose the appropriate proof method
Direct proof
Proof by contrapositive
Proof by contradiction
Proof by cases
Proof by induction
Existential proof
Uniqueness proof
Start from assumptions and derive the conclusion
Break complex statements into simpler parts
Apply known theorems and definitions carefully
Keep track of bound and free variables
Negate statements correctly when needed
Use quantifier rules correctly
Check each step for logical validity
Write proofs in a clear sequence of implications
Verify the final statement matches the goal
Practice with exercises from the book
Review common proof patterns
Review set notation and logic notation
Review relations, functions, and equivalence proofs
Review induction and recursion
Review contradiction and contrapositive techniques
Review proof structure for existence and uniqueness
Review how to prove set equality
Review how to prove subset relations
Review how to prove disjointness
Review how to prove divisibility statements
Review how to prove inequalities
Review how to prove statements about integers
Review how to prove statements about sets
Review how to prove statements about functions
Review how to prove statements about relations
Review how to prove statements about sequences
Review how to prove statements about sums and products
Review how to prove statements involving “if and only if”
Review how to prove statements involving “for all”
Review how to prove statements involving “there exists”
Review how to prove statements involving negations
Review how to prove statements involving nested quantifiers
Review how to prove statements involving multiple conditions
Review how to prove statements involving equivalence classes
Review how to prove statements involving mathematical induction
Review how to prove statements involving recursive definitions
Review how to prove statements involving cardinality
Review how to prove statements involving partitions
Review how to prove statements involving images and preimages
Review how to prove statements involving inverses
Review how to prove statements involving composition
Review how to prove statements involving injective, surjective, and bijective functions
Review how to prove statements involving reflexive, symmetric, and transitive relations
Review how to prove statements involving partial orders
Review how to prove statements involving equivalence relations
Review how to prove statements involving greatest common divisors
Review how to prove statements involving parity
Review how to prove statements involving modular arithmetic
Review how to prove statements involving real numbers
Review how to prove statements involving limits and continuity
Review how to prove statements involving sequences and series
Review how to prove statements involving finite and infinite sets
Review how to prove statements involving contradiction from assumptions
Review how to prove statements involving counterexamples
Review how to prove statements involving logical equivalence
Review how to prove statements involving tautologies and contradictions