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