# Subsets question

1. Oct 3, 2014

### HMPARTICLE

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".

Note;
I do know this is a simple question and i only just started my degree.

2. Oct 3, 2014

### LCKurtz

Your proof is fine, although you didn't need to subtract 4 and add it back. You could have just written$$y\ge (x+2)^2 = x^2 + 4x + 4 \ge 4x + 4$$

3. Oct 3, 2014

### HMPARTICLE

Thank you so much for the swift reply, PF never fails.