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Prove that f:X rarr Y is surjective iff ...

Prove that f:`X rarr Y` is surjective iff for all `A sube X,(f(A))' sube f(A')`, where A' denotes the complement of A in X.

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  2. Find the direction cosines of the line which is perpendicular to the l...

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  3. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

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  4. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  5. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  6. Find the points on the curve y = x^2+1 which are nearest to the point ...

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  7. Evaluate int0^ pi x/(1+ sin x) dx

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  8. Find the area of the regions into which the circle x^2+y^2=4 is divide...

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  9. Find the solution of the following differential equations: x dy-ydx=sq...

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  10. Show that hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) ...

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  11. A variable plane meets the coordinate axes at P, Q, R points. If the p...

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  12. Write whether the following statements are true or false. The equati...

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  13. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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  14. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  15. If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?

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  16. Find the extreme points of the function y= x+1/x.

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  17. What is the differential equation whose solution is y = c (sin x + cos...

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  18. For what value of lambda, the vectors lambda hat(i) + 3hat(j) + lambda...

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  19. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

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  20. Maximise Z=50x(1)+60x(2) Subject to 2x(1)+3x(2)le6,x(1),x(2)ge0.

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