PROPERTIES OF VECTORS - COMMUTATIVE AND ASSOCIATIVE

Division Of Integers|Properties Of Division Of Integers: Closure Property|Commutative Property|Division Of Zero|Division Identity|Associative Property|Distributive Property|Question Property|OMR

If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R . Then the operation ** is (i) Commutative but not associative. (ii) Associative but not commutative . (iii) Neither commutative nor associative . (iv) Both commutative and associative.

Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so, examine the commutative and association properties satisfied by * on A.

Properties Of Rational Numbers: Closure Property|Commutative Property|OMR

Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R defined as a*b|a-b| and a" "o" "b" "=" "a , AA""""a ," "b in R . Show that * is commutative but not associative, o is associative but not commutative.

Consider the binary operations ** \: R\ xx\ R -> R and o\ : R\ xx\ R -> R defined as a **\ b=|a-b| and aob=a for all a,\ b\ in R . Show that ** is commutative but not associative, o is associative but not commutative.

Properties Of Whole Numbers: Closure Property|Commutative Property|Associative Property|Distributive property|Identity For Addition|Identity For Multiplication

Properties Of Whole Numbers: Closure Property|Associative Property|Distributive property|Commutative Property|Identity For Addition|Identity For Multiplication

Consider a binary operation. on N defined 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?