Ans is B
First-order logic is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, thelower predicate calculus, quantification theory, and predicate logic. First-order logic uses quantified variables over (non-logical) objects. It allows the use of sentences that contain variables, so that rather than propositions such as Socrates is a man one can have expressions in the form X is a man where X is a variable. This distinguishes it frompropositional logic, which does not use quantifiers.
A theory about a topic is usually a first-order logic together with a specified domain of discourse over which the quantified variables range, finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axioms believed to hold for those things. Sometimes "theory" is understood in a more formal sense, which is just a set of sentences in first-order logic.