Define a commutative binary operation on a set.

Open in App

Solution

An operation * on a set A is called a commutative binary operation if and only if it is a binary operation as well as commutative, i.e. it must satisfy the following two conditions.

$(i) a * b \in A, \forall a, b \in A (Binary operation) (ii) a * b = b * a, \forall a, b \in A (Commutaive)$

Suggest Corrections

Similar questions

*

z

a * b = a - b + 2

*

Q

a * b = a b + 1,

*

For each binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(iv) On $Z^{+}$ , define $a * b = 2^{a b}$

For given binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(ii)On Q, define $a * b = a b + 1$

a^{*} b = a b^{3}

Join BYJU'S Learning Program