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Consider f: {1,2,3} to {a,b,c} and g: {a...

Consider `f: {1,2,3} to {a,b,c} and g: {a,b,c} to `{apple, ball, cat} defined as `f (1) =a, f (2) =b, f (3)=c, g (a)` = apple,` g (b) = ` ball and g (c )= cat. Show that f, g and gof are invertible. Find out `f ^(-1) , g ^(-1) and ("gof")^(-1)` and show that `("gof") ^(-1) =f ^(-1) og ^(-1).`

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Show that zero is the identity for addition on R and 1 is the identity...

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  17. Show that -a is the inverse of a for the addition operation '+' on R...

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  18. Show that -a is not the inverse of a in N for the addition operation...

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  19. If R1 and R2 are equivalence relations in a set A, show that R(1) cap...

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  20. Let R be a relation on the set A of ordered pairs of positive integers...

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