Interpreting: Consider S & T Sets - Are they Convex?

[matrixone]

Homework Statement

Homework Equations

The Attempt at a Solution

Consider S = {(1,1)} and T = {(0,0)}
Clearly, S and T is convex
S + T = S and S - T = S
So both of them are convex.
So answer is (E)

But i feel that the answer is too simple...and seems that i wrongly interpreted the question ...
Any thoughts?

 

[fresh_42]

What if you choose $T=\{(2,2)\}\,$? I assume the statement has to be true for any choice of $S,T$. And it didn't say, that they have to be convex. More interesting is if $S,T$ are balls (or squares, which are easier to handle in this case) of different radius and centers, what can be said then? Can this be generalized to convex sets with a non-empty interior?

 

[matrixone]

What if you choose $T=\{(2,2)\}\,$? I assume the statement has to be true for any choice of $S,T$. And it didn't say, that they have to be convex. But even if, and even if $S,T$ were balls (or squares, which are easier to handle in this case) of different radius and centers, what can be said then?

In the last line of the question, "Which of these is TRUE FOR ALL CONVEX SETS S & T? "

And, even if for only one choice of vertices, S & T both are convex, other options can be eliminated. Right ?

 

[fresh_42]

In the last line of the question, "Which of these is TRUE FOR ALL CONVEX SETS S & T? "

Sorry, overlooked. NO NEED TO USE CAPS.

And, even if for only one choice of vertices, S & T both are convex, other options can be eliminated. Right ?

An example isn't a proof. If you eliminate choices, you have to prove that it can be done without restricting the general case.

 

[Dick]

What if you choose $T=\{(2,2)\}\,$? I assume the statement has to be true for any choice of $S,T$. And it didn't say, that they have to be convex. More interesting is if $S,T$ are balls (or squares, which are easier to handle in this case) of different radius and centers, what can be said then? Can this be generalized to convex sets with a non-empty interior?

Actually the question does say "Which of the following is TRUE for all convex sets S and T?". I would suggest that you jump straight to trying to prove E... Might save you some time over looking at lots of a examples.