Negation follows systematic rules based on the connective: ~(p AND q) = ~p OR ~q (De Morgan's). ~(p OR q) = ~p AND ~q (De Morgan's). ~(p => q) = p AND ~q (not another implication). ~(p <=> q) = (p AND ~q) OR (~p AND q) = p XOR q. For statements with quantifiers: ~(for all x, P(x)) = there exists x, ~P(x). ~(there exists x, P(x)) = for all x, ~P(x). For complex nested statements, negate step by step from the outside in. Example: ~("All cats are black AND some dogs are white") = "Some cat is not black OR no dog is white." JEE problems phrase these in natural language, requiring students to translate, negate using formal rules, then translate back.