Mark the tick against the correct answer in the following: Let a * b

1.	Mark the tick against the correct answer in the following: Let a * b = a + ab for all a, b ∈ Q. Then, A. * is not a binary composition B. * is not commutative C. * is commutative but not associative D. * is both commutative and associative
Answer» *Correct Answer is (B) is not commutative According to the question ,** Q = { a,b } R = {(a, b) : a * b = a + ab } Formula * is commutative if a * b = b * a * is associative if (a * b) * c = a * (b * c) Check for commutative Consider , a * b = a + ab And , b * a = b + ba Both equations will not always be true . Therefore , * is not commutative ……. (1) Check for associative Consider , (a * b) * c = (a + ab) * c = a+ab + (a+ab)c=a+ab+ac+abc And , a * (b * c) = a * (b+bc) = a+a(b+bc) = a+ab+abc Both the equation are not the same and therefore will not always be true. Therefore , * is not associative ……. (2) Now , according to the equations (1) , (2) Correct option will be (B)

Mark the tick against the correct answer in the following: Let a * b = a + ab for all a, b ∈ Q. Then, A. * is not a binary composition B. * is not commutative C. * is commutative but not associative D. * is both commutative and associative

Answer»

Correct Answer is (B) * is not commutative

According to the question ,

Q = { a,b }

R = {(a, b) : a * b = a + ab }

Formula

* is commutative if a * b = b * a

* is associative if (a * b) * c = a * (b * c)

Check for commutative

Consider , a * b = a + ab

And , b * a = b + ba

Both equations will not always be true .

Therefore , * is not commutative ……. (1)

Check for associative

Consider , (a * b) * c = (a + ab) * c = a+ab + (a+ab)c=a+ab+ac+abc

And , a * (b * c) = a * (b+bc) = a+a(b+bc) = a+ab+abc

Both the equation are not the same and therefore will not always be true.

Therefore , * is not associative ……. (2)

Now , according to the equations (1) , (2)

Correct option will be (B)