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Prove that f:X to Y is injective iff for...

Prove that `f:X to Y` is injective iff for all subsets A, B of `X, f (A cap B) =f(A) cap f(B)`.

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Write the equation of the plane perpendicular to z-axis and passing th...

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  2. let f:ArarrB is a bijective function. Do you think f^(-1):BrarrA is al...

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  3. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

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  4. Find the number of equivalence, relations on X ={1,2,3),

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  5. Find the inverse of the following matrices using elementary transforma...

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  6. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  7. Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=...

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  8. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  9. Find the inverse of the following matrix [{:(0,0,2),(0,2,0),(2,0,0):}]

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  10. Examine the continuity of the following functions at indicated points....

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  11. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  12. Differentiate. x^(sin x)+(tan x)^x

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  13. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

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  14. etermine the sub-interval of (-(pi)/(2),(pi)/(2)), in which f(x)=tan x...

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  15. Integrate the following int(x+3)/(5-x^2-4x)

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  16. int0^2[x^2]dx

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  17. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  18. Solve the following differential equations (dy)/(dx)+(y)/(x)=x^(2), ...

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  19. Show that the vector area of the triangle whosse vertices have positio...

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  20. If the sum of two unit vectors is a unit vector, show that the magnitu...

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