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Let f: {1, 2, 3} rarr {a,b,c} be one-on...

Let `f: {1, 2, 3} rarr {a,b,c}` be one-one and onto function given by f(1) = a, f(2) = b and f(3) = C. Show that there exists a function `g: {a,b,c} rarr {1,2,3} ` such that gof `=I_(x) and fog = I_Y`, where X = {1,2,3} and Y = {a,b,c} ,

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Consider functions f and g such that composite gof is defined and is o...

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  2. Are fand g both necessarily onto, if gof is onto?

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

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  4. Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y...

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  5. Let Y = {n^(2) :n in N} subN Consider f: N rarr Y as f(n) = n^2 . Sh...

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  6. Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . ...

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  7. Consider f: N rarr N,g :N rarr N and h: Nrarr R defined as f(x) = 2x, ...

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  8. Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} de...

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  9. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  10. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  11. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  12. Show that addition, subtraction and multiplication are binary operatio...

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

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  14. Show that ** :Rxx R rarr R given by (a, b) rarr a + 4b^(2) is a bina...

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  15. Let P be the set of all subsets of a given set X. Show that cup: P xxP...

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  16. Show that the VV: RxxR rarr R given by (a, b) rarr max {a, b} and th...

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  17. Show that + : Rxx R rarr R and xx: R xxR rarr R are commutative binar...

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  18. Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commuta...

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  19. Show that addition and multiplication are associative binary operation...

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  20. Show that ""^** : R xxR rarr R given by a^** b rarr a + 2b is not ass...

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