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Show that subtraction and division are n...

Show that subtraction and division are not binary operations on N.

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Number of binary operations

Show that addition,subtraction and multiplication are binary operations on R, but division is not a binary operation on R . Further,show that division is a binary operation on the set R of nonzero real numbers.

Define a binary operation on a set.

Show that addition and multiplication are associative binary operation on R.But subtraction is not asociative on R.Division is not associative on R^(*).

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

Associativity of binary operations

Distributivity of binary operations

Commutativity of binary operations

Define a commutative binary operation on a set.

Which of the following is true? * defined by a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N

MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Objective Type Questions (D. Very Short Answer Types Questions)
  1. If f is a function from RrarrR such that f(x)=x^(2)AA x inR, then show...

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  2. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

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  3. The function P is defined as: ''To each person on the earth is assig...

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  4. Write the function whose graph is shown below:

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  5. Consider functions f and g such that composite gof is defined and i...

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  6. Are f and g both necessarily onto, if gofis onto?

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  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  8. Give examples of function: f:NrarrN and g:NrarrN such that gof is ...

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  9. Find fog, if f:RrarrR and g:RrarrR are given by: f(x)=cosxandg(x)=x^...

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  10. If f (x) = sin x, g(x) = x^(2), if x inR, then find [(fog)(x)].

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  11. If f:RrarrR is defined by f(x)=3x+1, find f(f(x)).

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  12. Let '**' be a binary operation on N given by: a**b=LCM (a,b) for all...

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  13. Let '**' be a binary operation on N given by: a**b=LCM (a,b) for all...

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  14. The binary operation **:RxxRrarrR is defined as: a**b=2a+b. Find (...

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  15. Show that + : R xx R ->Rand xx : R xx R ->Rare commutative binary ope...

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  16. Show that + : R xx R ->Rand xx : R xx R ->Rare commutative binary ope...

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  17. Show that addition and multiplication are associative binary operat...

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  18. Show that subtraction and division are not binary operations on N.

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  19. Show that " "a is not the inverse of a in N for the addition op...

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  20. Show that " "a is not the inverse of a in N for the addition op...

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