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Let A be a finite set. Then, each inject...

Let A be a finite set. Then, each injective function from A into itself is not surjective.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. True or False statements : Every function is invertible.

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  2. True or False statements : The relation R = (a,b), (ba,) on the set ...

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  3. Let A be a finite set. Then, each injective function from A into itsel...

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  4. True or False statements : Let A = (a,b,c) and R = (a,b),(a,c). Then...

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  5. The relation R on the set A = {1, 2, 3} defined as R = {(1, 1), (1, 2)...

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  6. The function f : R rarr R defined by f(x) = 1 + x^2 is :

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  7. Every relation which is symmetric and transitive is also reflexive.

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  8. True or False statements : Let N be the set of natural numbers. Then...

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  9. True or False statements : A binary operatio on a set has always the...

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  10. The function f : R rarr R defined by f(x) = 1 + x^2 is :

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  11. True or False statements : Let N be the set of natural numbers. Then...

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  12. True or False statements : The function f : R rarr R defined by f(x)...

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  13. Let A = {0, 1} and N be the set of natural numbers. Then the mapping f...

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  14. True or False statements : The binary operation * defined in Z by a ...

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  15. An integer m is said to be related to another integer n if m is a inte...

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  16. Let R be a relation from a set A to a set B, then:

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  17. True or False statements : Composition of functions is associative.

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  18. True or False statements : The function f : R rarr R defined by f(x)...

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  19. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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  20. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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