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Consider the binary operations *:" "RxxR...

Consider the binary operations `*:" "RxxR ->R` and `o:" "R" "xx" "R->R` defined as `a*b|a-b|` and `a" "o" "b" "=" "a , AA""""a ," "b in R` . Show that * is commutative but not associative, o is associative but not commutative. Further, show that `AAa

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The correct Answer is:
`a**(b o c)=(a**b)o(a**c)AAa,b,cinR`.
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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Revision Exercise
  1. Let f : X->Ybe a function. Define a relation R in X given by R = {(a ...

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  2. If R(1) and R(2) are equivalence relations in a set A, show that R(1) ...

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  3. Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R1 be a relation on X ...

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  4. Show that the number of equivalence relations on the set {1, 2, 3} ...

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  5. Let A={1,\ 2,\ 3} . Then, show that the number of relations containi...

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  6. Find the number of all one-one functions from set A = {1, 2, 3}to itse...

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  7. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

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  8. Give examples of two one-one functions f(1)andf(2) from R to R such th...

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  9. Show that if f1 and f2 are one-one maps from R to R , then the product...

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  10. Let f: A->A be a function such that fof=f . Show that f is onto if and...

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  11. Consider the identity function I(N):NrarrN defined as : I(N)(x)=xAAx...

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  12. Consider a function f:[0,pi/2]->R given by f(x)=sin x and g:[0,pi/2]->...

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  13. Find fof^(-1) and f^(-1) of for the function : f(x)=(1)/(x),xne0. Al...

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  14. Show that the number of binary operations on {1, 2}having 1 as identit...

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  15. Determine whether the following binary operation on the set N is assoc...

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  16. Determine which of the following binary operations on the set N are a...

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  17. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

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  18. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

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