Universal quantifier: "For all x in D, P(x)" asserts P(x) is true for every element of domain D. Existential quantifier: "There exists x in D such that P(x)" asserts at least one element satisfies P(x). Negation rules: ~(for all x, P(x)) = "there exists x such that ~P(x)" — to disprove a universal claim, find ONE counterexample. ~(there exists x, P(x)) = "for all x, ~P(x)" — to disprove an existence claim, show NO element works. Nested quantifiers: "for all x, there exists y, P(x,y)" means for each x there is a (possibly different) y. The order matters: "there exists y, for all x" is stronger (one y works for all x). JEE problems typically test single-level quantifier negation.