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On R-[1] , a binary operation * is defin...

On `R-[1]` , a binary operation * is defined by `a*b=a+b-a b` . Prove that * is commutative and associative. Find the identity element for * on `R-[1]dot` Also, prove that every element of `R-[1]` is invertible.

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
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  2. Consider the set S={1,-1,i ,-i} for fourth roots of unity. Construct t...

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  3. On R-[1] , a binary operation * is defined by a*b=a+b-a b . Prove that...

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  4. Let * be a binary operation on Q0 (set of non-zero rational numbers) ...

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  5. If the binary operation * on the set Z of integers is defined by a*...

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  6. Show that the operation vv and ^^ on R defined as avvb= Maximum of ...

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  7. Let n be a positive integer. Prove that the relation R on the set Z o...

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  8. Define a binary operation ** on the set A={1,\ 2,\ 3,4} as a**b=a b...

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  9. On the set R-{-1} a binary operation * is defined by a*b=a+b+a b for a...

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  10. Q^+ denote the set of all positive rational numbers. If the binary ope...

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  11. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  12. On the power set P of a non-empty set A, we define an operation * by ...

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  13. If the binary operation * on Z is defined by a*b=a^2-b^2+a b+4 , then ...

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  14. Is * defined by a*b=(a+b)/2 is binary operation on Z.

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  15. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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  16. On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity ...

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  17. Let +6 (addition modulo 6) be a binary operation on S={0,\ 1,\ 2,\ ...

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  18. Let A=Q x Q and let * be a binary operation on A defined by (a , b)*(c...

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  19. Let A=NxN , and let * be a binary operation on A defined by (a , b)*(...

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  20. Discuss the commutativity and associativity of binary operation * d...

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