Question #322

[AlexY297]

K will be selected if and only if L is not.

Answer choices

1) not K--> not L
or
2) not K-->L

Initially I thought that if and only if can be diagrammed both ways as sufficient and necessary ie. K --> Not L or L--> not K.

How is it that answer choice 2) not K-->L the correct answer?

Thank you,
Alex

[ohthatpatrick]

You're correct.
If and only if means "nec and suff", or "a double-head arrow", if you like to draw it that way.

What you just wrote out was akin to writing
A --> B
and
~B --> ~A

You wrote
K --> ~L
L --> ~K

But you were thinking you were writing out the two different conditionals given by "if and only if".
Instead, you were just writing one of the conditionals, and then writing its contrapositive.

Since K is both nec and suff, the two conditionals you get are
K --> ~L
and
~L --> K

If you wanted to write their contrapositives, you'd have
K --> ~L
L --> ~K
and
~L --> K
~K --> L

Or if you prefer, just write two lines with doublesided arrows.
K <---> ~L
~K <---> L

Hope this helps.