difference between first order and second order logic
Second-order logic First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence   ∀ P ∀ x ( x ∈ P ∨ x ∉ P )  {\displaystyle \forall P\,\forall x(x\in P\lor x\notin P)}  says that for every unary relation (or set) P of individuals, and every individual x, either x is in P or it is not (this is the principle of bivalence). Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.
Order of operations These mnemonics may be misleading when written this way,[6] especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would incorrectly evaluate the expression[6]