Symbolize the expression "Every mother loves her children" in predicate logic. Use predicates M(x): x is a mother, C(y,x): y is a child of x, L(x,y): x loves y.

GATE 1989 · Discrete Mathematics · First Order Logic · medium

Answer: forall x (M(x) -> forall y (C(y,x) -> L(x,y)))

1. Identify the outer universal claim: For every person x, if x is a mother, then the inner property must hold.
2. Expand 'her children' with a nested quantifier: For every person y, if y is a child of x, then x loves y. This fills in the inner '...' from Step 1.
3. Combine into the final formula: Joining steps 1 and 2 gives the complete symbolization.