Happy to try and help —
I think the confusion may stem from the visuals on page 457 — those words are meant to indicate when the subject matter is present — as in yes, there is a conditional statement here, or yes, they are talking about one thing being necessary for another — the list of words is not meant to give any indication as to the exact relationship or ordering of elements in a conditional statement (whether it’s X – > Y, or Y – > X etc.) — sorry if I didn’t make that clear enough —
My suggestion throughout the book is to think about all conditional statements you encounter in terms of the guarantees they represent — this is much more consistent with how top scorers naturally think, and I believe that this is a far easier and more effective method than trying to memorize/utilize equations based on indicator words and such (for more information, please check out lessons 13 and 18 again) —
Here are the various conditional statements you brought up where your answers differed from mine/ along with some explanation of how to think of the phrases in terms of guarantees:
From Drill 1 –
Leon will only attend if Sarah does not.
If Leon attends, what do we know for sure? Sarah must not have. And so L- > – S.
Let’s check it the other way — if Sarah doesn’t attend, does Leon have to? No, they can both be absent and it wouldn’t violate the rule.
From Drill 2
The public always adores those who win and do not brag about it.
If the public adores you, does it guarantee that you won and didn’t brag about it? No, it doesn’t — maybe they could adore you for a million different reasons (such as giving everyone a free house), and it wouldn’t violate the given rule.
If you win and don’t brag, will the public adore you? Yes, because the rule tells us they always do as long as you satisfy the criteria. So, the guarantee is that
W + don’ brag -> pub adores.
From Drill 3
Only those wearing uniforms are allowed to ride the bus.
Does this mean that if you are wearing a uniform you are guaranteed a ride on the bus? No — maybe there are other reasons (such as that you are carrying something illegal) why they won’t let you ride, and it wouldn’t violate this rule in any way.
However, if you are riding the bus, per this rule, you must be wearing a uniform.
R -> U.
From Drill 4
The doll can only wear a hat when it wears a purple dress.
Can the doll wear a purple dress but no hat? Sure. So, PD -> H is not a guarantee.
If the doll is wearing a hat, do we know for sure it must have on the purple dress? Yes.
So, H -> PD is the given guarantee.
For Drill 5
Only wood that is not cut to exact dimensions is currently discounted.
So, if you have a piece of wood not cut to exact dimensions, does the above guarantee that it must be discounted? No, you could have an undiscounted piece of such wood without violating the rule.
If you have a piece of wood currently discounted, do we know for sure that it is wood not cut to exact dimensions? Yes we do, because only that type of wood is currently discounted.
So, D -> not ED.
Hope that helps —