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Sets and axioms

  1. Jan 12, 2010 #1
    Let a and b be sets. Show that the following constructions are sets stating clearly which axioms you need

    (a) a\b.

    (b) A function f:a→ b.

    (c) The image of f.

    (d) Given that a and b have ranks α and β respectively, what are the maximum possible ranks of a\b, f:a→ b and the image of f?

    I'm not sure of an answer for b and d at the moment.

    For (a) i'm thinking ab= {x∈a: x is not in b} and therefore is a set by the subset axiom

    and for (c) i'm thinking the image is {x∈b: there exists a y∈a, f(y)=x} which is a set by the subset axiom

    What do you think?
  2. jcsd
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