PT74.S4.Q23 (G4) - The manager of a photography business

practicethepause

Hello 7sagers,

I've been trying to make sense of this question for the longest time but I just can't seem to understand what the difference between answer choice (c) and (e) is.

Here's my train of thought.

We all know from the core curriculum that A unless B is
~A~ ---> B
OR
~B~ --> A

Given this, (c) states "Unless K is assigned to T, both F and M must be assigned to T."
(e) states, "Unless either H or M is assigned to T, K must be assigned to T."

So to put (c) into lawgic and if I put it in ~A~ --> B form, it reads, ~Ft and Mt~ --> Kt. If I were to do the contrapositive, it reads, ~Kt~ --> Ft or Mt.

Is this contrapositive right? The answer says that it's supposed to be contraposed back into ~Kt~ --> Ft and Mt but I seriously cannot understand why that would become an "and" statement...

But if I were to put it in the ~B~ --> A form, it reads, ~Kt~ --> Ft and Mt (which is the correct answer). I'm really confused as to why these two are coming out differently when it shouldn't be...

Please help! I feel like I'm not understanding the most basic concept of lawgic and it's truly giving me so much anxiety.

Admin note: edited title
https://7sage.com/lsat_explanations/lsat-74-section-2-game-4

Claire Z.

Hi Practice, I'm not sure if I'll be able to help but I know how bad the anxious feeling is so I will try.

The difference between C and E is that C says --Kt-- will result in BOTH Ft and Mt, whereas E says --Kt-- will result in EITHER Ht OR Mt.

Here is the diagramming if you want:

"Unless" can be translated "if not." C says: "If not Kt then both Ft and Mt," or "--Kt-- --> Ft and Mt." Contraposed it is "--Ft-- or --Mt-- --> Kt."

E says: "If not (Ht or Mt) then Kt," or "--Ht-- and --Mt-- --> Kt." Contraposed it is --Kt-- --> Ht or Mt.

The "not" in E gets distributed over the parentheses and turns the or into an and.

Here's a practical example. Unless Sammy either helps the teacher or washes the blackboard, he will receive a demerit.

If Sammy doesn't help the teacher AND doesn't wash the blackboard, he's getting the demerit.

If he didn't get the demerit, you can be certain he either helped the teacher or washed the blackboard. Or both.

I hope that helps.

practicethepause

Thank you so much for your response Claire! Reading "unless" as "if not" makes so much sense to me!

But then does that mean that writing A unless B as ~A~ ---> B wrong to use in this situation? Because "if not" is basically ~B~ --> A (but this is the same thing as ~A~ ---> B because they are contrapositives of each other).

To describe my confusion further, if I were to apply the ~A~ ---> B to (c), I would get ~Ft and Mt~ --> Kt. If I were to do the contrapositive of this, wouldn't it be ~Kt~ --> Ft or Mt ?

But the answer says it comes out to ~Kt~ --> Ft and Mt. Why is that?

I'm still slightly confused over this question

Claire Z.

It looks like you might be diagramming it backward. Are you applying the "if not" to the wrong half of the sentence?

Here is C showing all work:
Unless K is t --> both F and M are t
Unless Kt --> both Ft and Mt
If not Kt --> both Ft and Mt
--Kt-- --> FtMt

Contrapositive:
--Ft-- or --Mt-- --> Kt

Does that help?