# Binary operation: Quiz

Question 1: Thus, for the general, non-associative case, binary operations can be represented with ________.
B-treeTree (data structure)Binary treeBinary tree (data structure)

Question 2: Binary operations are the keystone of algebraic structures studied in ________: they form part of groups, monoids, semigroups, rings, and more.
Abstract algebraVector spaceNumber theoryCategory theory

Question 3: Note that the ________ of two vectors is not a binary operation, external or otherwise, as it maps from S × S to K, where K is a field and S is a vector space over K.
Inner product spaceEuclidean vectorDot productCross product

Question 4: Examples include the familiar arithmetic operations of ________, subtraction, multiplication and division.

Question 5: If the operation is associative, (ab)c=a(bc), then the value depends only on the ________ (a,b,c).
Set theorySet (mathematics)TupleNatural number

Question 6: If the operation is commutative, ab=ba, then the value depends only on the ________ { {a,b},c}.
Binomial coefficientSet (mathematics)MultisetFunction (mathematics)

Question 7: Examples of partial operations that are not commutative include division (/), ________(^), and super-exponentiation(↑↑).
Complex numberLogarithmVector spaceExponentiation

Question 8: Sometimes, especially in ________, the term is used for any binary function.

Question 9: In ________, a binary operation is a calculation involving two operands, in other words, an operation whose arity is two.
MathematicsMathematical logicGeometrySet theory

Question 10: Typical examples of binary operations are the ________ (+) and multiplication (×) of numbers and matrices as well as composition of functions on a single set.