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On Z ** defined by a**b = a+b+1 . Is ** ...

On Z `**` defined by `a**b = a+b+1` . Is `**` associative ? Find identity element and inverse if it exists.

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The correct Answer is:
Yes, Identity element `=-1,a^(-1)=-2-a`
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Practice Work
  1. On R - {-1}, a binary operation ** defined by a"*"b = a + b +ab then f...

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  2. ** be a binary operation on a set {0,1,2,3,4} defined by a**b={(a+b,...

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  3. On Z ** defined by a**b = a+b+1 . Is ** associative ? Find identity el...

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  4. ** be binary operation defined on a set R by a**b=a+b-(ab)^2. Show tha...

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  5. A binary operation ** be defined on the set R by a**b = a+b +ab. Show ...

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  6. Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr ...

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  7. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

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  8. f : R rarr R , f(x) = cos x and g : R rarr R , g(x) = 3x^(2) then fin...

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  9. Check the injectivity and surjectivity of the following function . f...

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  10. Check the injectivity and surjectivity of the following function . f...

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  11. Check the injectivity and surjectivity of the following function . f...

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  12. Check the injectivity and surjectivity of the following function . f...

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  13. Check the injectivity and surjectivity of the following function . f...

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  14. Check the injectivity and surjectivity of the following function . f...

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  15. f: R rarr (-1, 1) , f(x) = (10^(x)-10^(x))/(10^(x)+10^(-x)). If inver...

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  16. f: R^(+)cup{0} rarrR^(+)cup{0},f(x) = sqrtx. g : R rarr R , g(x)=x^...

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  17. f: R - {2/3} rarr R , f(x) = (4x+3)/(6x-4). Prove that (fof) (x) = x ,...

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  18. A = {1,2,3,4} , B = {1,5,9,11,15,16} f = {(1,5),(2,9),(3,1),(4,5),(2...

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  19. A = {1,2,3,4} , B = {1,5,9,11,15,16} f = {(1,5),(2,9),(3,1),(4,5),(2...

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  20. Let f be the subset of Z xx Z defined by f={(ab,a+b) : a,b in Z}. Is f...

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