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# Conditional statement

Member
12 karma

I have a random question LMAO! If in a grouping logic game the rule is: if W then T or F
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

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• Core Member
6 karma

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").

• Yearly Member
edited November 2021 238 karma

@pam2198 said:
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.

@k_bains11 said:
I have a random question LMAO! If in a grouping logic game the rule is: if W then T or F
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

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 must be the truth value of W, and what does that imply for truth value of F?

• Core Member
edited November 2021 350 karma

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 sufficient to trigger “T or F”, but it’s not necessary.

“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!)