Which is a counterexample for the conditional statement shown? If three distinct points lie in a plane, then the points can form a triangle....

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erato erato · Answer 1 · 2019-07-03T12:33:01+02:00

We take the example of:

Three collinear points in a plane.

Then we may conclude that they will never form a triangle.

We know that a conditional statement is given by:

If p then q

where p is the hypothesis of the statement and q is the conclusion of the statement.

Counter example for a conditional statement--

A counter example is an example that makes the general statement is false.

i.e. a example which fulfills the condition of the hypothesis but does not satisfy the conclusion of the given statement.

If three distinct points lie in a plane, then the points can form a triangle.

i.e. Hypothesis is: Three distinct point lie in a plane.

and conclusion is: The points form a triangle.

So we take a example as:

Three collinear points lie in a plane but they will never form a triangle.

facundo3141592 facundo3141592 · Answer 2 · 2021-09-17T22:33:36+02:00

For a given conditional statement:

If P then Q,

A counterexample would be a case where P is true and Q is not.

Here the counterexample is: "3 collinear points on the plane can't make a triangle."

Now let's see how to get that:

The conditional statement is just:

"If three distinct points lie in a plane, then the points can form a triangle"

So to find a counterexample, we need to find a set of 3 points that lie on a plane that do not form a triangle.

This is kinda trivial, but if we have 3 collinear points, then these points can't make any triangle.

An image of this can be seen below.

So the counterexample is "3 collinear points on the plane"

If you want to learn more, you can read:

https://brainly.com/question/88496