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    Boundness of sets

    How to prove that set of real numbers is unbounded?
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    Integration using integrating factor

    Homework Statement Integrate dy/dx=2y+4x+10 The Attempt at a Solution dy/dx-2y=4x+10 Integrating factor = e^(-2)dx=e^-2x multiply both sides by IF. (e^-2x)dy/dx-2y(e^-2x)=(e^-2x)(4x+10) dy/dx(e^-2x y)=(e^-2x)(4x+10) i dont know what to do next.
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    Counter examples to disprove mappings?

    give counter examples to disprove the following statements: a) a real valued odd function cannot be strictly monotonic b) a real valued periodic function must be odd or even c) a real valued monotonic function cannot be even a) sinh(x) ?? b) c)
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    Give example of matrices such that AB=AC but B=/=C

    [b]1. Let M(2,R) be the set of all 2 x 2 matrics over R. Give an example of matrices A,B,C in M(2,R) such that AB=AC, but B is not equal to C. [b]3.
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    Groups and subgroups

    [b]1. Let G be a group containing subgroups H and K such that we can find an element h e H-K an an element k e K - H. Prove that h o k is not a subgroup of H U K. Deduce that H U K is not a subgroup of G. I have proved that h o k is not in H U K but I dont know how to deduce that H U K is not...