070912 Biconditionals and Definitions

 

Write the converse of this conditional and determine the truth value of each. 

 

If two lines intersect to from right angles, then they are perpendicular.

 

 

 

 

When a conditional and itÕs converse are both true, both statements can be combined to form what is called a ÔBiconditionalÕ.  What does this mean?  A biconditional, in a nutshell, says that for one to be true, the other must be true and vice versa. The two statements above can be written as:

 

Two lines intersect to form right angles if and only if they are perpendicular.

 

Can you write this statement in reverse order and still have the same meaning?:

 

 

 

How about this statement:

 

X^2 = 100 if and only if x = 10.

 

Is this statement a Ôtrue biconditionalÕ?

 

 

Now what about definitions?

 

Here is a definition of ÔbookÕ

 

book:  A book is something that you read.,

 

Is this a good definition? 

 

 

What properties can make a good definition?

 

 

 

How about some of the definitions we have in our Book of Knowledge?  Here are some terms we have defined during the past 4 weeks.   For each term, write itÕs definition from the Book of Knowledge, and answer the questions that follow.

 

Distance from a point to a line:

 

 

 

a.       Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.  (Hint:  First write the statement as a conditional, then itÕs converse.  Determine the truth value of each, and write the biconditional)

 

 

 

 

 

 

 

 

 

 

Equidistant Point:

 

 

a.       Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.

 

 

 

 

 

Midpoint:

 

 

 

 

a.        Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.

 

 

 

Segment Bisector:

 

 

 

a.       Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.

 

 

 

 

 

Perpendicular Bisector:

 

 

a.       Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.

 

 

 

 

 

 

 

Circle:

 

 

 

a.       Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.

 

 

 

 

 

 

 

Angle Bisector:

 

 

 

a.       Are the words we used easily understandable?

 

b.      Is the definition precise?

 

c.       Write the definition as a biconditional.