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k_bains11
Member

does that mean that if I have T or F in the yes/in group, I must have W as well

or can I have T or F without the W

## Comments

No, W does not have to be in the group. You can have T or F without W, but based on your wording, both T and F would mean that W has to be out ("if W, then T OR F").

That assumes "or" to be an exclusive or (

viz.xor), which we cannot assume, b/c there's nothing in the original post to suggest that.As initially phrase, and assuming "or" to be standard or (as in, one, the other, or both), W --> (T or F) is really a nested conditional (parentheses necessary because order of operation in logical statements go from right to left).

What it is saying is that assuming W is true, then one of T and F has to also be true (

viz.T & F cannot be both out when W is true).It's essentially saying, if it's not the case that W implies T, then it is the case that W implies F.

In conditional form, it is 1) /(W --> F) --> (W --> T), which is the equivalence of 2) ((W --> F) or (W -->T)) and 3) /(W --> T) --> (W --> F)).

As to your original questions, if either of T and F is true, the nested conditional is rendered irrelevant. I'll demonstrate for T, but you should repeat the exercise for F and then for T & F.

If T is true, W --> T is automatically true (necessary statement of a conditional satisfied). Since (W --> T) is itself the necessary statement of the larger nested conditional, the entire nested conditional is also true. W & F can then be anything, because the nested conditional has been satisfied (by virtue of W --> T being true).

You may say, but what about forms 2) and 3) of the statement. While I could respond that because forms 2) and 3) are equivalents of form 1), so that I don't need to show additional proof, I think it's instructive to show what happens when T in the sufficient part in form 3) is true.

If T is true, then W --> T is true. Which makes /(W --> T) false. As /(W --> T) is the sufficient part of a larger nested conditional, making the sufficient of this nested conditional false satisfies the entire nested conditional. W & F can then be anything.

Now here's a question for you, what's the implication if T is in the out group? To make this easier, what

mustbe the truth value of W, and what does that imply for truth value of F?On the LSAT if “or” is exclusive they will say “A or B but not both”. If they don’t say that it’s exclusive, you should assume you can have both.

You can have T or F or both without W. As a conditional, W is

sufficientto trigger “T or F”, but it’s notnecessary.“If I (take a Kaplan course) then (I will improve my score 3 points) or (I will get zero wrong on logic games).”

The Kaplan course is sufficient for the improvement, but it’s not necessary. After all, you could increase your score with a different tutoring company (like 7sage!)