## Understanding Necessary and Sufficient Conditions....

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ccordero

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Joined: Wed May 23, 2012 3:14 pm

### Understanding Necessary and Sufficient Conditions....

Can anyone please help me understand necessary and sufficient conditions? I'm reading through the LR Bible and there is a chapter on Cause and Effect Reasoning, with a section that marks the difference between causality and conditionality.

Basically it says that causality implies that the cause makes the effect happen. I understand this (obviously)

But I can't seem to wrap my head around the connection between the necessary and sufficient conditions. I understand that with causality, the cause must occur first before the effect. If a necessary condition is "an event whose occurrence is required in order for a sufficient condition to occur," then how could a sufficient condition occur before a necessary condition?

From the Powerscore LR Bible: "In conditional statements the sufficient and necessary conditions are often related directly, but they do not have to be: 'Before the war can end, I must eat this ice cream cone.' The sufficient condition does not make the necessary condition happen, it just indicates that it must occur."

(I don't know if I'm allowed to post an excerpt from a book so please someone tell me if I cannot do this, and I will edit it out right away. I apologize in advance if I'm not allowed to...)

I am really trying to wrap my head around how both the chronology between events and the connection between events of conditional reasoning is supposed to make sense.... can anyone help?

bhan87

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Joined: Mon Mar 12, 2007 8:08 pm

### Re: Understanding Necessary and Sufficient Conditions....

Argument: I have exactly \$1.00 in my pocket.

Sufficient, but not Necessary Conditions:

- I have four quarters in my pocket.
- I have 10 dimes in my pocket.
- I have 20 nickels in my pocket.

In each of these cases, the condition being true means the argument must be true. However, because there are multiple different conditions that can make the argument true, none of them are necessary.

Necessary, but not Sufficient Conditions:

- I have more than \$.50 in my pocket
- I do not have a \$20 bill in my pocket

In both these cases, the condition being true DOES NOT mean that the argument must be true. However, both are absolutely necessary for the argument to be true. The best way to think about this is if the condition was false, what effect would it have on the argument. For instance, if I did not have more than \$.50 in my pocket, I couldn't have exactly \$1.00

03152016

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Joined: Wed Dec 21, 2011 3:14 am

### Re: Understanding Necessary and Sufficient Conditions....

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Last edited by 03152016 on Tue Mar 15, 2016 3:02 am, edited 1 time in total.

LSATSCORES2012

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Joined: Mon Jul 02, 2012 2:12 pm

### Re: Understanding Necessary and Sufficient Conditions....

The way I remember it is this:

A sufficient condition is *sufficient* to ensure a certain result.

A necessary condition is *necessary* given a certain factor.

Consider the statement If X, then Y.

If you have X, it is necessary that you have Y.

X is sufficient to ensure Y.

Don't know if this will help or if it just sounds like nonsense, but that's what helped me out.

bp shinners

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Joined: Wed Mar 16, 2011 7:05 pm

### Re: Understanding Necessary and Sufficient Conditions....

Sufficient/necessary conditions are much harder for people to wrap their heads around than causality.

With causality, I know that one thing made the other thing happen. So if I set my foot on fire, that will cause me to burn. That's a relationship that makes sense to people - I do something, it has an effect.

Conditionals are weird because they don't imply that the two things are part of a causal chain. Instead, it's just relating two different things. Don't think of it as a description of reality; think of it as a rule being asserted.

The basic example is "If there's smoke, there's fire." This is what the PS Bible is talking about when it says that the statements are related. I know that smoke and fire often come together. I also know that fire causes smoke, not the other way around. Regardless, this conditional is telling me that if I see smoke, that is sufficient to tell me there's a fire. That's not true - plenty of ways to get smoke without a fire - but I accept it as a general rule for this question on the LSAT.

It gets a little weirder when I have two things that aren't related, and it makes people's heads hurt. "If I wear my lucky green underwear, the Simpsons will get good again." These two things have nothing to do with each other. However, this rule is being asserted, and I just have to accept it as true - when I don my Irish boxers, then it must also be true that the Simpsons will improve in quality.

So causality is essentially dealing with how we view the real world - one thing happens, which causes another thing to happen, etc...

Conditionality is just asserting rules that you have to mindlessly follow - one thing happens, and for some reason that I don't really care about, something else must happen.

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