Conditional: If point M is the midpoint of segment AB, then point M is between points A and B. .

Question

Conditional: If point M is the midpoint of segment AB, then point M is between points A and B.

For the given conditional statement, determine which of the following option(s) has a truth value of true. Select all that apply.

         Conditional
Converse
Inverse
Contrapositive

Answer 1

Hi Kristen,

 

The converse of p->q is q->p. For this case: if M is between points A and B, then M is the midpoint of seg AB. 

 

False as illustrated by: A-----M--------------B

 

The inverse is represented by not p -> not q. If M is not the midpoint of seg AB, then M is NOT between A and B.

 

False: A-------------------M----B

 

Contrapositive: not Q -> not P. If M is not between A and B, then M is not the midpoint of seg AB.

 

True: M----A-------B. If M is not between it for sure cannot be the midpoint. 

 

The contrapositive of an implication/conditional is always logically equivalent to the original. 

Answer 2

If the conditional is true, the converse it not necessarily true. And in this case it is false.

The inverse is false, the point can be not a midpoint and be between.

The contrapositive is always true.