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 kumarshe
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#26017
Hello,

I had question about one of the side notes on pg. 277 of the 2016 edition of the bible.

"Note that any compound sufficient condition that uses "or" can be turned into two separate arrow diagrams." I understand this part, however, the second part confuses me: "Similarly, any compound necessary condition that uses "and" can be turned into two separate arrow diagrams...
I just don't understand how "and" in the necessary can become two separate statements.

- Shefali
 Robert Carroll
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#26018
Shefali,

Imagine we have this case:

"If A is included, both B and C are included."

This means that A is sufficient for B, and A is also sufficient for C. Thus, the conditional can be split into two diagrams:

A :arrow: B

A :arrow: C

Robert Carroll
 kumarshe
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#26039
I still can't wrap my head around it. I just can't get the concept.
I understand that if X or Y :arrow: Z there can be two separate, individual sufficient causes for Z.
Therefore X :arrow: Z and Y :arrow: Z.
I also understand how X and Y :arrow: Z (because the joint occurrence forces the necessary to occur)

I'm just can't get how X :arrow: Y or Z can't be broken up into two statements.
From my understanding it seems like if X occurs then either Y or Z could occur, therefore, we could have two separate statements.
Similarly, I can't figure out why X :arrow: Y and Z can occur as two separate statements. It seems like if X occurs then Y + Z must occur together. How can they be separated. I read the blog post on Diagramming LSAT Conditional Statements 101: "And" in the Necessary Condition but still don't understand.
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 Dave Killoran
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#26097
kumarshe wrote:I'm just can't get how X :arrow: Y or Z can't be broken up into two statements.
From my understanding it seems like if X occurs then either Y or Z could occur, therefore, we could have two separate statements.
Similarly, I can't figure out why X :arrow: Y and Z can occur as two separate statements. It seems like if X occurs then Y + Z must occur together. How can they be separated.
Hey Shefali,

Thanks for the followup! I quoted the statement above because you seem to be good up until that point.

In the first statement above, the nature of "or" is the problem, and it is the reason why it can't be separated into two statements like the others. That statement says that if you have X, you must have at least one of Y or Z. Well, you can't know which of the two will appear, so it can't be separated. Consider the following example:

  • "If you go to the store, you must buy milk or cookies."

    Diagrammed, this appears as:

    ..... ..... ..... Milk
    ..... Store :arrow: or
    ..... ..... ..... Cookies

    Now, to separate this into two statements, you would change it to:

    ..... Store :arrow: Milk

    ..... Store :arrow: Cookies

    The problem is that while each statement could be true, each doesn't have to always be true. For example, in the case of Store :arrow: Milk, does that always happen? No, because if the person went to the store and bought cookies, the initial statement would be satisfied. So, you can't separate this into two separate statements that are individually true at all times.

    It may help to understand that we're not just trying to separate the statements into possible outcomes, but rather into outcomes that always occur when the sufficient condition occurs. We can actually separate any statement into sub parts, but we don't do it if the outcomes only occur sometimes (as is the case here). The value is in separating a statement into sub-statements that always occur when the sufficient occurs.
Moving on to the next statement (X :arrow: Y and Z), let's again use our example:

  • "If you go to the store, you must buy milk and cookies."

    Diagrammed, this appears as:

    ..... ..... ..... Milk
    ..... Store :arrow: +
    ..... ..... ..... Cookies

    Now, to separate this into two statements, you would change it to:

    ..... Store :arrow: Milk

    ..... Store :arrow: Cookies

    Now, in the case of Store :arrow: Milk, does that always happen? Yes! and the same is true for Store :arrow: Cookies, and so each stands alone as constant, true statement when the sufficient condition occurs. That's why we are able to separate them out.

Ultimately, your ability to separate these statement rests on which operator ("or" / "and") appears in which condition. If "or" appears in the sufficient, you can separate it and have each statement be individually true. If "and" appears in the necessary, you can separate that as well. But if "or" appears in the necessary, or if "and" appears in the sufficient," then you cannot separate them. It's very tricky.

And just for more confirmation, I wrote two blogs about these topics, at:


Please let me know if that helps. Thanks!
 kumarshe
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#26105
Thanks Dave! It makes sense now!! :-D

Thanks,

Shefali
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 Dave Killoran
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#26134
Great, glad I could help!

Also, in order to keep questions from different games and drills in different threads, I move your question about page 300 over here: lsat/viewtopic.php?f=7&t=10874.

Thanks!
 leslie7
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#83030
I had the same question and this breakdown was very helpful - ty so much.

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