What is the relation between commutativity and associativity?

Open in App

Solution

Associative Property The word "associative" comes from "associate" or "group"; the Associative Property is the rule that refers to grouping. For addition, the rule is "a + (b + c) = (a + b) + c"; in numbers, this means 2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4. Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Propert Commutative Property
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.

Suggest Corrections

Similar questions

Q. Subtraction of integers is
(a) commutative but no associative
(b) commutative and associative
(c) associative but not commutative
(d) neither commutative nor associative

Q. Consider a binary operation * on N defined as a * b = a 3 + b 3 . Choose the correct answer. (A) Is * both associative and commutative? (B) Is * commutative but not associative? (C) Is * associative but not commutative? (D) Is * neither commutative nor associative?

Q. Let * be a binary operation on R defined by a * b = ab + 1. Then, * is
(a) commutative but not associative
(b) associative but not commutative
(c) neither commutative nor associative
(d) both commutative and associative

Consider a binary operation $*$ on N defind as $a * b = a^{3} + b^{3}$ . Choose the correct answer.
$(a) *$ both associative and commutative
$(b) *$ commutative but not associative
$(c) *$ is associative but not commutative
$(d) *$ is neither commutative nor associative

Consider a binary operation * on N defined as a * b = a³ + b³. Choose the correct answer.

(A) Is * both associative and commutative?

(B) Is * commutative but not associative?

(D) Is * neither commutative nor associative?

Join BYJU'S Learning Program