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.
are there choices for the counterexamples, or do we make one up?
these are the choices: Counterexample: If four points are non-coplanar, they still may be collinear. If and only if four points are non-collinear are they non-coplanar. Four points are non-coplanar if and only if they are non-collinear. Counterexample: Four points may be non-collinear and yet lie in the same plane.
ok, well we know that points that are coplanar are on the same plane and colinear points are on the same line. If four points are non-coplanar, then they are non-collinear. true. if they aren't on the same plane, how could they be on the same line? If four points are non-collinear, then they are non-coplanar. false. Counterexample: Four points may be non-collinear and yet lie in the same plane.
do you understand that?
yes
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