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Homework Help: Subsets question

  1. Oct 3, 2014 #1
    1. The problem statement.
    consider the following sets;
    1. C = {(x, y) ∈ R^2 : y ≥ (x + 2)^2},

      D = {(x, y) ∈ R^2 : y ≥ 4x + 4}.
    show that C is a subset of D.

    3. Attempt at solution.

    Let (x,y) be an arbitrary element of C, then

    y ≥ x^2 + 4x + 4.

    Rearranging the inequality gives

    y - 4 ≥ x^2 + 4x.

    Now since x^2 ≥ 0 for all x in R. This implies that

    y -4 ≥ 4x. Hence y ≥ 4x+4. As required.

    Now my gut instinct is that i am totally wrong with this. I am just starting my degree and usually find these questions quite easy.
    I have tried various other manipulations but to no avail :(. If i must be honest i have "forced it".

    I do know this is a simple question and i only just started my degree.
  2. jcsd
  3. Oct 3, 2014 #2


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    Gold Member

    Your proof is fine, although you didn't need to subtract 4 and add it back. You could have just written$$
    y\ge (x+2)^2 = x^2 + 4x + 4 \ge 4x + 4$$
  4. Oct 3, 2014 #3
    Thank you so much for the swift reply, PF never fails.
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