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A binary operation ast on Z defined by...

A binary operation `ast` on `Z` defined by `a ast b=3a+b` for all `a ,\ b in Z` , is (a) commutative (b) associative (c) not commutative (d) commutative and associative

A

(a) commutative

B

(b) associative

C

(c) not commutative

D

(d) commutative and associative

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Verified by Experts

The correct Answer is:
(c) not commutative
For commutativity
Let, `a,b in Z`
`a ast b =3a+b`
`b ast a=3b +a`
`a ast b ne b ast a`
Not commutative

For associativity
Let, `a,b,c in Z`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  8. Subtraction of integers is

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  9. The law a+b=b+a is called

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  10. An operation * is defined on the set Z of non-zero integers by a*b=a/...

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  11. On Z an operation * is defined by a * b=a^2+b^2 for all a ,\ b in Z...

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  12. A binary operation ast on Z defined by a ast b=3a+b for all a ,\ b i...

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  13. Letastbe a binary operation on N defined by a ast b=a+b+10 for all a...

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  14. Consider the binary operation ast defined on Q-{1} by the rule a ast...

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  15. For the binary operation ast defined on R-{-1} by the rule a ast b=a...

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  16. For the multiplication of matrices as a binary operation on the set ...

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  17. On the set Q^+ of all positive rational numbers a binary operation *...

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  18. Let ast be a binary operation defined on Q^+ by the rule a ast b=(a...

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  19. The number of binary operations that can be defined on a set of 2 el...

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  20. The number of commutative binary operations that can be defined on a...

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