Question: 3 . Determine whether the following statement is TRUE or FALSE. If it is TRUE, briefly explain why. If it is FALSE, provide a counterexample

3 .

Determine whether the following statement is TRUE or FALSE. If it is TRUE, briefly explain why. If it is FALSE, provide a counterexample that disproves the statement.

(1)

A set of

9

points in the plane is given. You are told that every triple of these points lies inside a disk of radius

1 .

All

9

points lie inside a single disk of radius

1 . (2)

You are given

6

points in the plane. It is known that every

4

of them lie in a disk of radius

1,

but not necessarily every

3 .

All

6

points lie in a disk of radius

1 .

3 . Determine whether the following statement is

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