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Define a binary operation * on the set...

Define a binary operation * on the set `A={0,\ 1,\ 2,\ 3,\ 4,\ 5}` as a * b=a+b(mod 6) Show that zero is the identity for this operation and each element `a` of the set is invertible with `6-a` being the inverse of `adot`

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Define a binary operation ** on the set {0, 1, 2, 3, 4, 5} as a**b={a+b if a+b<6; a+b-6,if a+b geq 6 . Show that zero is the identity for this operation and each element a !=0 of the set is invertible with 6-a being the inverse of a

Define a binary operation ** on the set A={1,\ 2,\ 3,4} as a**b=a b\ (mod\ 5) . Show that 1 is the identity for ** and all elements of the set A are invertible with 2^(-1)=3 and 4^(-1)=4.

A binary operation * on the set {0,1,2,3,4,5} is defined as: a * b={a+b ,a+b-6"\ \ \ \ if\ "a+b<6"\ \ \ if"\ a+bgeq6 Show that zero is the identity for this operation and each element a of the set is invertible with 6-a, being the inverse of a.

Define a binary operation * on the set A={0,1,2,3,4,5} given by a\**b=a b (mod 6) . Show that 1 is the identity for *. 1 and 5 are the only invertible elements with 1^(-1)=1 and 5^(-1)=5

Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a b (mod 6). Show that 1 is the identity for *. 1 and 5 are the only invertible elements with 1^(-1)=1 and 5^(-1)=5

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The binary operation defined on the set z of all integers as a ** b = |a-b| - 1 is

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let * be a binary operation on set of integers I, defined by a*b=2a+b-...

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  2. Discuss the commutativity and associativity of the binary operation * ...

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  3. Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as ...

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  4. Consider the set S={1,-1,i ,-i} for fourth roots of unity. Construct t...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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