Let $*: R \times R \rightarrow R$ be def

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let $*: R \times R \rightarrow R$ be defined by $a* b=a+2 b$. Then * is

Options:

associative

commutative

commutative and associative

not commutative

Correct Answer:

not commutative

Explanation:

The correct answer is Option (4) - not commutative

$a*b=a+2 b$

$(a* b)*c=a+2 b+2c$

while $a*(b*c)=a+2(b+2c)$

Not Associative as $(a* b)*c≠a*(b*c)$

$a* b=a+2b,b*a=b+2a$

$a+2b≠b+2a$ ⇒ not commutative