Splitting figures on the Cartesian plane

What is the minimum number of lines to separate the sets?

a) 2 b) 3 c) 4 d) 1 e) 5

Observe the graph below, it is possible to separate linearly with a line at least two of the classes?

a) Yes, just pass a straight line on the vertical axis.
b) Yes, just pass a straight line on the horizontal axis.
c) Yes, with all points separated.
d) No, because the classes mix.
e) No, because there are four quadrants.

How many circles are needed to group all points into three groups with 2
points and a group with 4 points?

a) 3 circles
b) 5 circles
c) 4 circles
d) Points would remain
e) There is no answer

I believe the answers are

1. 3
2. No, because the classes mix
3. Points would remain

These challenges were proposed to me by a discreet math teacher and, as they are "challenges", I don’t imagine that the answers are so simple.

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