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If ** be the binary operation on the set...

If `**` be the binary operation on the set `ZZ` of all integers, defined by `a**b=a+3b^(2)`, find `2**4.`

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(I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. (ii) let ** be a binary operation on RR-{-1} , defined by a**b=(1)/(b+1) for all a,binRR-{-1} Show that ** is neither commutative nor associative. (iii) Let ** be a binary operation on the set QQ of all raional numbers, defined as a**b=(2a-b^(2)) for all a,binQQ . Find 3**5 and 5**3 . Is 3**5=5**3?

let ** be a binary operation on ZZ^(+) , the set of positive integers, defined by a**b=a^(b) for all a,binZZ^(+) . Prove that ** is neither commutative nor associative on ZZ^(+) .

Let ** be a binary operation on NN , the set of natural numbers defined by a**b=a^(b) for all a,binNN is ** associative or commutative on NN ?

let ** be a binary operation on RR , the set of real numbers, defined by a@b=sqrt(a^(2)+b^(2)) for all a,binRR . Prove that the binary operation @ is commutative as well as associative.

Let @ be a binary operation on QQ , the set of rational numbers, defined by a@b=(1)/(8)ab for all a,binQQ . Prove that @ is commutive as well as associative.

A binary operation ** on QQ , the set of rational numbers, is defined by a**b=(a-b)/(3) fo rall a,binQQ . Show that the binary opearation ** is neither commutative nor associative on QQ .

If the binary operation on ZZ is defined by a**b=a^(2)-b^(2)+ab+4, then the value of (2**3)**4 is --

Show that an operation ** on RR , the set of real numbers, defined by a**b=3ab+sqrt2, for all a,binRR . Is a binary operaion on RR.

If the binary operation ** on the set ZZ is defined by a**b=a+b-5 , then the identity element with respect to ** is K . Find the value of K .

Show that the operation ** on ZZ , the set of integers, defined by. a**b=a+b-2 for all a,b inZZ (i) is a binary operation: (ii) satisfies commutaitve and associative laws: (iii) Find the identity elemetn in ZZ , (iv) Also find the inverse of an element ainZZ.

CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. (I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. ...

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  2. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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  3. If ** be the binary operation on the set ZZ of all integers, defined b...

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  4. A binary operation @ is defined on ZZ, the set of integers, by a@b=|a-...

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  5. Let ** a binary operation on NN given by a**b=H.C.F (a,b) for all a,bi...

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  6. If +(6) (addition modulo 6) is a binary operation on A={0,1,2,3,4,5},...

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  7. A binary operation ** is defined on the set RR(0) for all non- zero re...

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  8. A binary operation ** is defined on the set ZZ of all integers by a@b=...

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  9. A binary operation ** is defined on the set of real numbers RR by a**b...

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  10. For the binary operation multiplication modulo 5*(xx(5)) defined on th...

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  11. A binary operation ** on QQ the set of all rational numbers is defined...

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  12. Prove that the identity element of the binary opeartion ** on RR defin...

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  13. Find the identity element of the binary operation ** on ZZ defined by ...

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  14. The binary operation * define on N by a*b = a+b+ab for all a,binN is

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  15. Prove that 0 is the identity element of the binary operation ** on ZZ^...

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  16. A binary operation ** on QQ(0), the set of all non-zero rational numbe...

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  17. A binary operation @ on QQ-{1} is defined by a**b=a+b-ab for all a,bin...

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  18. A binary operation ** on QQ, the set of rational numbers, is defined b...

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  19. Determine which of the following binary operations are associative and...

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  20. Let S be any set containing more than two elements. A binary operation...

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