How to diagram statements with "if and only if"

[hnadgauda]

On page 69 of the LR Strategy Guide for Question #3, A and B use the phrases "if and only if". How are we supposed to diagram these statements?

Thank you!

[ohthatpatrick]

People tend to diagram
if and only if
if but only if
then and only then
when and only when

with a double-sided arrow.


I will go to Jen's party if and only if she makes fondue.

Go to party <----> makes fondue

When you write a contrapositive, it doesn't really matter whether you FLIP-and-negate, because the arrow goes both ways.

So you could write

~makes fondue <----> ~go to party
or
~go to party <----> ~makes fondue

Some people prefer to think of all these bi-conditionals as either/ors. Either both things happen or both things don't.

So you could also just represent a bi-conditional as creating two worlds

WORLD 1
Go to party/makes fondue
WORLD 2
doesn't go to party/doesn't make fondue