Symbolize the expression "Every mother loves her children" in predicate logic.

Question

Accepted Answer

forall x [ M(x) -> forall y ( C(y, x) -> L(x, y) ) ], equivalently forall x forall y ( (M(x) AND C(y, x)) -> L(x, y) ). The English sentence makes a claim about all mothers, so the outermost word is the universal quantifier forall. Inside, for any mother we again talk about all of her children, so a second forall appears. The trick is that 'her children' is a conditional relationship: only the things that ARE children of that mother are claimed to be loved, so we attach the loving claim with an implication, not a plain AND.