How can I determine if a set is convex without graphing it?

I have that a set, , is convex if, given any two points, , the line connecting them is entirely within , or:

Some of the sets in question:

b.

c.

d.

e.

f.

I have to hand in f. I'm not good enough to draw it, but I can envision it. It looks like a "V" going from down to . Clearly, it is not convex. But how would I show that mathematically?

Thanks.