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Let A and B be two sets with a finite nu...

Let A and B be two sets with a finite number of elements. Assume that there is injective mapping from A to B and that there is an injective mapping from B to A. Prove that there is a bijective mapping from A to B.

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ML KHANNA-CONCEPTS OF SET THEORY -Problem Set (3) (FUNCTIONS AND MAPPING)
  1. Let f: R to R be defined by f(x) = 3x + 4, X in R Is f invertible ? ...

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  2. The composite mapping fog of the maps f:R to R , f(x)=sin x and g:R to...

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  3. Let A and B be two sets with a finite number of elements. Assume that ...

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  4. If f: R to R is defined by f (x)= x^2 + 1, then values of f^(-1) (17) ...

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  5. Which of the statements given below is different from the other?

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  6. Find the domain and range of f (x)= x^2 //(1+x^2)(x real). Is the func...

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  7. If A={x:-1lexle1} and f be a function on A. Discuss the following func...

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  8. If A={x:-1lexle1}=B. Discuss the following functions w.r.t. one-one-on...

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  9. Let f:AtoA where A={x:-1lexle1}. Find whether the following function a...

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  10. If f :A-> A,A={x:-1lexle1}=B. Discuss the following functions w.r.t. o...

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  11. If f :A-> A,A={x:-1lexle1}=B. Discuss the following functions w.r.t. o...

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  12. Set A has 3 elements and set B has 4 elements. The number of injection...

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  13. The number of surjections from A={1,2,... n}, n ge 2, onto B = {a,b} ...

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  14. Let A and B be two finite sets having m and n elements respectively. T...

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  15. The total number of injective mappings from a set with melements to a ...

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  16. Let A be a set containing 10 distinct elements, then the total number ...

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  17. If the mappings f : A to B and g: B to C are both bijective, then th...

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  18. Let E = {1,2,3,4} and F {1,2}. Then the number of onto functions from ...

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  19. Let A = {0,1} and N the set of all natural numbers. Then the mapping ...

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  20. Let f be an injective map with domain {x,y,z) and range {1,2,3} such t...

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