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Show that :-R xx RrarrR and div : R xx R...

Show that :-`R xx RrarrR` and `div : R xx R rarrR ` are not commutative binary operations.

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Show that +: R xx R rarr R and xx : R xx R rarr R are commutative binary operations.

Show that +:RxxRrarrR and xx:RxxRrarrR are commutative binary operations, but -:RxxRrarrR and -::RxxRrarrR are not commutative.

Show that * : R × RrarrR defined by a * b = a + 2b is not commutative.

Show that * : R xx R rarr R given by a * b rarr a + 2b is nto associative.

Show that subtraction and division are not associative binary operations on R.

Show that vv : R xx R rarr R given by (a, b) rarr max. [a, b) and ^^: R xx R rarr R given by (a, b) rarr min (a, b) are binary operations.

Show that addition and multiplication are associative binary operations on R.

Show that addition and multiplication are associative binary operation on R. But subtraction is not associative on R. Division is not associative on R_∗ .

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Show that :-R xx RrarrR and div : R xx R rarrR are not commutative bi...

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  2. Which one of the following graph represents the function of x? Why?

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  3. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be onto...

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  4. Let A be the set of all 50 students of class XII in a school. Let f: A...

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  5. Prove that the function f : RrarrR given by f (x) = 2x is one-one and...

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  6. Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x...

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  7. Show that function f: Rrarr R given by f(x) = x^2 is neither one-one n...

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  8. Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,i...

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  9. If f : R rarr R is defined by f(x) = x + 2, find f(f(x))

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  10. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

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  11. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

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  12. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find gof.

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  13. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

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  14. Let f(x) = (4x+3)/(6x-4), x ne 2/3 .show that fof (x) = x.

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  15. Find gof and fog if f: RrarrR and g: R rarr R are given by f(x) = co...

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  16. If the function f : R rarr R given by f(x) = x^2 +2 and g RrarrR be g...

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  17. Let f : { 1, 2, 3} rarr {a, b, c} be one-one and onto function given b...

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  18. Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by ...

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  19. Let Y = {n^2 : n in N} sub N Consider f : N rarr Y as f (n) = n^2 Show...

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  20. Let f: Nrar R be a function defined as : f(x) = 4x^2 + 12 x + 15. Sho...

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  21. Let f : N rarr N be a function deifned by f(x) = 9x^2 + 6x - 5. Show ...

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