Question

Rewrite the following definition as a biconditional:

Points that lie on the same line are collinear.

Answer 1

Do you know how to write "Points that lie on the same line are collinear." in the If, then" format?

Answer 2

yeah

Answer 3

So how would it read? What we need to do is to get P->Q and then its converse to form the biconditional.

Answer 4

"if points lie on the same line, then they are collinear" tada lol

Answer 5

P: if points lie on the same line
q:then they are collinear
That's p>q

Okay, how would the converse of p->q be written?

Answer 6

thats what i dont know :/

Answer 7

wait does it go " if they are collinear then the points are on the same line"?

Answer 8

The converse of p-> q is q ->p.
Look above where I wrote the designations for p and q. Then, write If the q part, the the p part. That would be the converse.

Answer 9

Definition: A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow . The biconditional p<->q represents "p if and only if q," where p is a hypothesis and q is a conclusion.

Answer 10

wait does it go " if they are collinear then the points are on the same line"?
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YES, that's correct. Read the definition of biconditonal and we can wrap up this problem.

Answer 11

Note on "if they are collinear then the points are on the same line"?"

Not only is it the correct form of the converse, it is a true statement as is the original statement. So .... it's a biconditional.

Answer 12

k

Answer 13

Biconditional Form: Points on the same line <--> ?
You add the second part.

Answer 14

are collinear

Answer 15

Points on the same line <--> collinear points.
That's how I would phrase it.

Answer 16

thanks for your help! :)