Question

Determine if the conditional and its converse are true. If they are both true, select which biconditional correctly represents them. If either the conditional or the converse is false, select the counterexample which disproves the statement:
If four points are non-coplanar, then they are non-collinear.
If four points are non-collinear, then they are non-coplanar.

Answer 1

The conditional,  If four points are non-coplanar, then they are non-collinear, is true:

This is, coplanarity is a necessary condition to be collinear.

The converse, If four points are non-collinear, then they are non-coplanar, is false.

A counterexample that disproves this statement is the 4 vertices of a paralelogram, of course they are in a same plane and are not collinear.