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Hi. I have a question regarding sufficient and necessary conditions. Let's say I have something like: If R and N are in, then T is out. In this case, am I able to split this to R is in, then T is out and N is in T is out? Or, would I need an OR instead of an AND to do this? Additionally, if I have something like: If R is in, then T and N are out, can I split this to say, if R is in, then T is out and if R is in, then N is out. Thank you.

Mylovejoy wrote:Hi. I have a question regarding sufficient and necessary conditions. Let's say I have something like: If R and N are in, then T is out. In this case, am I able to split this to R is in, then T is out and N is in T is out? Or, would I need an OR instead of an AND to do this? Additionally, if I have something like: If R is in, then T and N are out, can I split this to say, if R is in, then T is out and if R is in, then N is out. Thank you.

In the first case you have to satisfy the sufficient condition so you can't split up the "and" when it's on the sufficient side:
Example: if J and K go to the party THEN L will. Both J and K must go in order for the sufficient side to be triggered so you can't write K THEN L or J THEN L.

In the second case you would be able to split since AND is on th necessary side. Example: If J goes to the party THEN K and L will. So if J goes we know that K goes, and if J goes we know that L goes. So you can split them up.

To summarize, when AND is on the sufficient side you can't split it up but when it's on the Necessary side you can.
When OR is on th sufficient side you can split it up, but not when OR is on the necessary side (since you'd be implying that both have to go).Think about this logically and it'll make sense.

Mylovejoy wrote:Hi. I have a question regarding sufficient and necessary conditions. Let's say I have something like: If R and N are in, then T is out. In this case, am I able to split this to R is in, then T is out and N is in T is out? Or, would I need an OR instead of an AND to do this? Additionally, if I have something like: If R is in, then T and N are out, can I split this to say, if R is in, then T is out and if R is in, then N is out. Thank you.

It says R and N are in, then T is out. You cant split that. You could if it said R or N.

Mylovejoy wrote:Hi. I have a question regarding sufficient and necessary conditions. Let's say I have something like: If R and N are in, then T is out. In this case, am I able to split this to R is in, then T is out and N is in T is out? Or, would I need an OR instead of an AND to do this? Additionally, if I have something like: If R is in, then T and N are out, can I split this to say, if R is in, then T is out and if R is in, then N is out. Thank you.

In the first case, you can't split that statement into those two. In the second case, you can. It all has to do with the placement of the word "and."

1) R & N --> not T

Think about what this is saying. The sufficient condition, which has to be met in order to guarantee the necessary condition, is that BOTH R and N are in. If we just know that one of them is in, that isn't equivalent to the sufficient condition, so we can't be sure if T is out or in. We need to meet the full requirements of the sufficient condition.

Another way to think about it is to flip it into its contrapositive. The contrapositive is just another way of representing the same statement. In conditional statements that use "and" or "or", you have to exchange those words for each other. So an "and" will become an "or," and vice versa. In this case, the contrapositive is:

T --> not R OR not N

This is telling us that if T is in, then at least one out of R and N MUST be out. The thing to remember about "or" on the LSAT is that it is not the exclusive "or" that we're used to hearing in everyday speech. "Or" on the LSAT could mean both, so if T is in, both R and N and could both be out. We don't know that for sure, but it's important to know that it is a possibliity.

2) R --> not T & not N

In this case, the sufficient condition has a less stringent requirement. Only one variable, R, has to be in for us to guarantee the necessary condition. So if R is in, T is out, and if R is in, N is also out. Satisfying the sufficient condition means that everything in the necessary condition MUST happen, so this works.

The contrapositive, in this case, is:

T OR N --> not R

If either T or N (or both, remember!) are in, then R is out. This makes sense, right? If R were in, then both of those two would have to be out, so if either of them are in fact in, then there's no way that R could be in.

To continue the discussion of whether or not we can split statements, we can indeed split this one as well. If T is in, that satisfies the sufficient condition T or N, so T --> not R is true. The same goes for N --> not R.

Hope that helps!