Exercise 28 Page 88

Practice makes perfect

a An if-then statement contains a hypothesis and conclusion. The Plane-Point Postulate states that a plane contains at least three noncollinear points. This means if we start with a plane, our hypothesis, we are able to place at least three noncollinear points on it, our conclusion. With this, we can write the postulate in if-then form.

If there is a plane then it contains at least three noncollinear points

b Let's go through the conditional statements one at a time.

Converse

The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement. If there are at least three noncollinear points, then we can draw a plane.

This is true for the same reason the Plane-Point Postulate is true.

Inverse

The inverse of a conditional statement, ~ p→ ~ q, requires us to negate the hypothesis and the conclusion of the conditional statement. If there is not a plane then it does not contain at least three noncollinear points This is also true for the same reason the Plane-Point Postulate is true. We cannot have a plane without at least three noncollinear points.

Contrapositive

The contrapositive of a conditional statement, ~ q→ ~ p, is similar to the converse except we have to negate both the hypothesis and the conclusion. If there are not at least three noncollinear points, then we cannot draw a plane. This is true for the same reason the inverse is true. We need at least three noncollinear points to have a plane.

Subchapter links

Communicate Your Answer p.83

Monitoring Progress p.85-86

Exercises p.87-88

Exercise 28 Page 88

Hints

Check the answer

Practice exercises

Asses your skill

Converse

Inverse

Contrapositive