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Prove that for binary operation defined on R such that ab=a+`4b^(2)` is not associative

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ARIHANT PUBLICATION-RELATIONS AND FUNCTIONS -CHAPTER PRACTICE (Very Short Answer Type Questions )
  1. Let A = {1,2,3,4,…., 15,16} and let R be a relation in A given by R={...

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  2. If the relation R is defined on the set A={1,2,3,4,5} by R={a,b} : |a^...

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  3. State the reason for the relation R in the set {1, 2, 3} given by R ={...

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  4. Show that the function f: R rarr R , f(x)=x^(4) is many-one and into.

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  5. If f(x)=27x^(3) and g(x) =x^(1//3). Then, find gof(x).

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  6. If f: R rarr R is defined by f(x) = 3x + 2 define f (f (x))

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  7. Write fog if f:R rarr R and g: R rarr R is given by f(x) = | x| and g(...

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  8. Find gof and fog, if f: R rarr R and g: R rarr R are given by f(x) = c...

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  9. If A= {a,b,c,d) and the function f = {(a,b),(b,d), (c,a), (d,c)}, then...

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  10. If f is an invertible function, defined as f(x)= (3x-4)/(5) then write...

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  11. Let* is a binary operation on the set of all non-zero real numbers, gi...

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  12. If the binary operation on the set of integers Z, defined by a b= a +3...

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  13. Show that * On Z^(+) defined by a*b = |a-b| is a binary operation or n...

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  14. Show that * On R defined by a*b = a +4b^(2) is a binary operation or n...

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  15. For each binary operation defined below, determine whether * is the co...

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  16. For each binary operation defined below, determine whether * is the co...

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  17. Prove that for binary operation defined on R such that ab=a+4b^(2) is ...

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  18. For each binary operation * defined below, determine the identity elem...

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  19. For each binary operation * defined below, determine the identity elem...

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