# Reply To: \"Extreme links\" (pg. 460-461) – Extreme confusion!

January 18, 2017 at 4:05 pm #2952
Mike Kim
Keymaster

Hi Mia,

Here are three different ways to think about the conditional statement —

“The doll can only wear a hat when it wears a purple dress.”

I hope they help clear things up —

1) Thinking about the statement in terms of guarantees —

The functional purpose of a conditional statement is to represent a guarantee — if one thing is true, the other thing must be true.

For PD -> H to be a correct, that would mean that per the above statement, wearing a purple dress guarantees that the doll has on a hat.

With that in mind, it can help to read the statement —

“The doll can only wear a hat when it wears a purple dress”

and ask yourself —

“Does this statement guarantee that if the doll wears a purple dress, it must wear a hat?” If you don’t see such a guarantee in the statement, than you know that PD -> H can’t be correct.

2) A more technical explanation

“The doll can only wear a hat when it wears a purple dress” is akin to

“The doll can wear a hat only when it wears a purple dress” is akin to

“The doll can wear a heat only if it wears a purple dress.”

“Only if” is a fairly common phrase, and “X only if Y” is correctly translated as “X -> Y.”

3) With an analogy

“The doll can only wear a hat when it wears a purple dress” is akin to

“We can only watch programs on the television when it is plugged in.”

Does this mean that if a TV is plugged in you must watch it? No.

Does this phrase mean that if you were able to watch TV it was plugged in?

Yes, so you could translate it Watched -> Plugged in.

Relating this back to the doll example —

“We can only watch programs on the television when it is plugged in” =

W -> P

“The doll can only wear a hat when it wears a purple dress” =

H -> PD

Again, hope that helps clear things up — take care — Mike