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Prove that the following sets are equiva...

Prove that the following sets are equivalent
{1, 2, 3, 4, 5, 6.....}, (2, 4, 6, 8, 10,...)
(1,3,5, 7, 9,...), {1, 4, 9, 16, 25...)

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Let h: `A rarr D` defined as `h(x) = x^2` Clearly h is bijective.
`implies` There is a one-to-one correspondence between A to D.
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MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. Prove that {1,2,3,4,5,6,……} set are equivalent.

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  2. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  3. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  4. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  5. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  6. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  7. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

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  8. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  9. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-...

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  10. Let f(x) = sqrt(x) and g(x) = 1 -x^(2). Show that hgof only on R(0)=...

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  11. Find the composition fog and gof and test whether fog = gof when f and...

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  12. Find the composition fog and gof and test whether fog = gof when f and...

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  13. Find the composition fog and gof and test whether fog = gof when f and...

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  14. Find the composition fog and gof and test whether fog = gof when f and...

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  15. Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even...

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  16. Express each of 1+x+x^2 function as the sum of an even function and an...

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  17. Express each of x^2 function as the sum of an even function and an odd...

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  18. Express each of e^x function as the sum of an even function and an odd...

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  19. Express each of e^x+ sin x function as the sum of an even function and...

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  20. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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