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Let A be the set of all 50 students of...

Let `A` be the set of all 50 students of class `X I I` in a central school. Let `f: A->N` be a function defined by `f(x)="Roll number of student x"` Show that `f` is one-one but not onto.

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`f(x) ="Roll number of students x"`
`"One one" `
`f(x_1)="roll number of students " x_1`
`f(x_2)="roll number of students " x_2`
...
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NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Prove that the function f : R ->R, given by f (x) = 2x, is one-one and...

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  2. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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  3. Let A be the set of all 50 students of class X I I in a central scho...

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  4. Show that the relation R in the set {1, 2, 3}given by R = {(1, 1), (2...

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  5. Show that the relation R on the set Z of integers, given by R={(a ,\ b...

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  6. Let "T" be the set of all triangles in a plane with "R" as relation ...

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  7. Let L be the set of all lines in a plane and R be the relation in L de...

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  8. Let A be the set of all students of a boys school. Show that the rela...

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  9. Show that – a is the inverse of a for the addition operation '+' on R ...

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

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  11. Show that the vv: R ->R given by (a , b)->m a x {a , b}and the ^^: R -...

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  12. Let P be the set of all subsets of a given set X. Show that uu: P xx ...

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  13. Show that ∗ : RxxR->R given by (a ,b)->a+4b^2is a binary operation.

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

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  15. Show that *: Rxx R ->Rgiven by a*b = a +2bis not associative.

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  16. Show that addition and multiplication are associative binary operatio...

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  17. Show that *: R xxR ->Rdefined by a*b = a +2bis not commutative.

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  18. Show that + : R xx R ->R and xx : R xx R ->R are commutative binary ...

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  19. Let Y = {n^2: n in N} in N. Consider f : N ->Yas f(n)=n^2. Show tha...

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  20. Let f : N ->R be a function defined as f(x)=4x^2+12 x+15. Show that f...

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