## Multiple Necessary/Sufficient Conditions

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HarvardHopeful93

Posts: 68
Joined: Wed Apr 11, 2012 6:30 pm

### Multiple Necessary/Sufficient Conditions

Having a little trouble with these at the moment. Specifically looking at Grouping Game #1 on p.223 of PowerScore's LG Bible.

So if we have a multiple sufficient condition rule (say, G AND S -> W), we cannot infer two separate rules like G -> W and S -> W, right?

But with a multiple necessary condition, we can? Say we have N -> R AND S , then we can infer that N -> R and N -> S, right?

Is this true? 7Sage's video for the logic game got me thinking about this when he drew two arrows from N to each of R and S, but I've always just written out the rule with one arrow.

Is it because of the nature of conditionals? Help?

kevgogators

Posts: 160
Joined: Mon May 19, 2014 11:34 pm

### Re: Multiple Necessary/Sufficient Conditions

HarvardHopeful93 wrote:Having a little trouble with these at the moment. Specifically looking at Grouping Game #1 on p.223 of PowerScore's LG Bible.

So if we have a multiple sufficient condition rule (say, G AND S -> W), we cannot infer two separate rules like G -> W and S -> W, right?

But with a multiple necessary condition, we can? Say we have N -> R AND S , then we can infer that N -> R and N -> S, right?

Is this true? 7Sage's video for the logic game got me thinking about this when he drew two arrows from N to each of R and S, but I've always just written out the rule with one arrow.

Is it because of the nature of conditionals? Help?

You got it right.

If the rule is G and S ---> W, but only G is in, is it necessary for W to also be in? Nope! The rule isn't triggered.
Likewise, if only S is in, but not G, is it NECESSARY for W to be in? No. It could, but doesn't have to be. Again, the rule isn't triggered.

However,
If the rule is N --> R and S, then we know that as long as N is in, both R and S MUST be in. The rule is triggered! Some people prefer to split these type of rules into two for clarity.

So if N --> R
Also if N -->S

I think you might be tripping yourself up between "and" versus "or"...

Had the rule been : G or S ---> W, then it would've been correct to infer G -> W and S -> W. Either of them would trigger the rule there!

Make sense?

HarvardHopeful93

Posts: 68
Joined: Wed Apr 11, 2012 6:30 pm

### Re: Multiple Necessary/Sufficient Conditions

Thank you, thank you!!! Yes, that helps a lot. Now I just have to master grouping games.

I think you're right though, my weakness seems to be the inference side of the equation. Do most folks use the "double not arrow" that Powerscore suggests? Or do they just write out the conditional and contrapose it? I noticed Ping from 7sage just writes out the conditional. But PS seems to know what they're doing...