Direct proof: Assume the hypothesis p is true, then use logical steps to derive the conclusion q. This is the most straightforward method. Proof by contrapositive: Instead of proving p => q, prove ~q => ~p (logically equivalent). Useful when the negation of the conclusion provides more workable information. Proof by contradiction: Assume the statement is false (i.e., assume ~(p => q), which is p AND ~q), then derive a contradiction (something that is always false). The contradiction proves the original statement must be true. Proof by counterexample: To disprove a universal statement "for all x, P(x)", find ONE specific x where P(x) is false. JEE tests understanding of these methods through questions about the logical structure of arguments rather than requiring students to write full proofs.